We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Solving Triangles

Study concepts, example questions & explanations for Trigonometry

Create An Account

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Finding Angles

A 15 foot plank has one end on the ground and one end 6 feet off the ground. What is the measure of the angle formed by the plank and the ground?

Possible Answers:

$\approx 50^{\circ}$

$\approx 70^{\circ}$

$\approx 10^{\circ}$

$\approx 24^{\circ}$

Correct answer:

$\approx 24^{\circ}$

Explanation:

The length of the plank becomes the hypotenuse of the triangle, while the distance between the plank and the ground becomes the length of one side. To solve for the angle between the plank and the ground, you must find the value of $sin (\angle )$ . The sine of the angle is the value of the opposite side over the hypotenuse, which are values that we know.

$sin(\angle )= \frac{opposite}{hypotenuse} = \frac{6}{15}$

$\angle =sin^{-1} \frac{6}{15} = 24^{\circ}$

Report an Error

Example Question #1 : Finding Angles

Two angles in a triangle are $30^\circ$ and $70^\circ$ . What is the measure of the 3rd angle?

Possible Answers:

$100^\circ$

$90^\circ$

There is not enough information to determine the angle measure.

$80^\circ$

$70^\circ$

Correct answer:

$80^\circ$

Explanation:

The sum of the angles of a triangle is 180˚.

Thus, since the sum of our two angles is 100˚, our missing angle must be,

180 - 100 = 80 .

Report an Error

Example Question #2 : Finding Angles

If the hypotenuse of a right triangle has a length of 6, and the length of a leg is 2, what is the angle between the hypotenuse and the leg?

Possible Answers:

$4.87^\circ$

$19.47^\circ$

$13.54^\circ$

$32.12^\circ$

$70.53^\circ$

Correct answer:

$70.53^\circ$

Explanation:

The leg must be an adjacent side to the hypotenuse.

Therefore, we can use inverse cosine to solve for the angle.

First write the equation for sine of an angle.

$cos(\theta)=\frac{\textup{Adjacent}}{\textup{Hypotenuse}}$

$\theta=cos^{-1}\left(\frac{\textup{Adjacent}}{\textup{Hypotenuse}}\right)$

Substitute the lengths given and solve for the angle.

$\theta=cos^{-1}\left(\frac{\textup{2}}{\textup{6}}\right)=70.53^\circ$

Report an Error

Example Question #3 : Finding Angles

A skateboard ramp made so that the rider can gain sufficient speed before a jump is 15 feet high and the ramp is 17 feet long. What is the measure of the angle $\theta$ between the ramp and the ground?

Possible Answers:

$\theta=70.4^{\circ}$

$\theta=62^{\circ}$

$\theta=20^{\circ}$

$\theta=34.2^{\circ}$

None of the other answers.

Correct answer:

$\theta=62^{\circ}$

Explanation:

For the angle in question we have the opposite side and the hypotenuse given to us. We can use the sine function.

$\sin\theta= \frac{opp}{hyp}\rightarrow\sin\theta=(\frac{15}{17})$

Use the inverse sin to find the measure of an angle between these sides:

$\theta =\sin^{-1}(\frac{15}{17})=62^{\circ}$

Report an Error

Example Question #2 : Finding Angles

What angle does the ramp make with the bottom of the stair?

Screen_shot_2014-02-15_at_3.16.35_pm

Possible Answers:

33.7^o

30^o

45.0^o

$\small 28.9^o$

56.3^o

Correct answer:

33.7^o

Explanation:

$\small tan(c)=\frac{c}{a}=\frac{2}{3}$

$\small tan(c)=\frac{2}{3}$

$\small c=tan^{-1}(\frac{2}{3})$

c=33.7^o

Report an Error

Example Question #1 : Solving Triangles

Given that angle A is 23.0^o, side a is 1.43 in., and side b is 3.62 in., what is the angle of B?

Screen shot 2014 02 15 at 3.41.09 pm

Possible Answers:

70^o

81.5^o

83.6^o

55^o

90^o

Correct answer:

81.5^o

Explanation:

$\small \small \small \frac{sin(23.0^o)}{1.43\: in.}=\frac{sin(B)}{3.62\: in.}$

$\small \small \small \sin(B)=\frac{3.62 in.\times \sin(23.0^o)}{1.43 in.}$

$\small \small \small \sin(B)=0.99$

$\small B=sin^{-1}(0.99)$

$\small B=81.5^o$

Report an Error

Example Question #367 : Trigonometry

Artemis wants to build a ramp to make the entrance to their home more accessible. The angle between the ramp and the ground cannot be more than $7^\circ$ steep. Artemis has feet of space in their yard that the ramp can take up, and the distance between the ground and the house entrance is feet high. Will Artemis be able to build a ramp that complies with the $\leq7^\circ$ standard?

Possible Answers:

Yes

Correct answer:

Explanation:

Begin the problem by visualizing a diagram of the situation:

Screen shot 2020 08 09 at 3.36.03 pm

We can use inverse trig to solve for the unknown angle $\theta$ .

$\tan\theta=\frac{3}{12}$

$\theta=\tan^-^1\left (\frac{3}{12} \right )$

$\theta=14.04^\circ$

Because this angle is larger than $7^\circ$ , this ramp would not comply with standards.

Report an Error

Example Question #368 : Trigonometry

If the hypotenuse of a right triangle has a length of 42.29 meters, and the length of a leg is 12.88 meters, what is the angle between the hypotenuse and the leg?

Possible Answers:

$15.15^\circ$

$14.64^\circ$

$74.85^\circ$

$99.99^\circ$

Correct answer:

$74.85^\circ$

Explanation:

The leg must be an adjacent side to the hypotenuse.

Therefore, we can use inverse cosine to solve for the angle.

First write the equation for sine of an angle.

$cos(\theta)=\frac{\textup{Adjacent}}{\textup{Hypotenuse}}$

$\theta=cos^{-1}\left(\frac{\textup{Adjacent}}{\textup{Hypotenuse}}\right)$

Substitute the lengths given and solve for the angle.

$\theta=cos^-^1\left (\frac{12.88}{49.29} \right )=74.85^\circ$

Report an Error

Example Question #1 : Finding Sides

If the height of the stair is 2 ft, and the length of the stair is 3 ft, how long must the ramp be to cover the stair?

Screen_shot_2014-02-15_at_2.24.54_pm

Possible Answers:

5 ft

10 ft

2.5 ft

13 ft

3.6 ft

Correct answer:

3.6 ft

Explanation:

Use the Pythagorean triangle to solve for the third side of the triangle.

a^2+b^2=c^2

2^2+3^2=13

$\therefore c^2=13$

$c=\sqrt{13}$

Simplify and you have the answer:

c=3.6 ft

Report an Error

Example Question #2 : Finding Sides

A surveyor looks up to the top of a mountain at an angle of 35 degrees. If the surveyor is 2400 feet from the base of the mountain, how tall is the mountain (to the nearest tenth of a foot)?

Possible Answers:

3427.6 feet

1966.0 feet

1376.6 feet

2135.8 feet

1680.5 feet

Correct answer:

1680.5 feet

Explanation:

This is a typical angle of elevation problem.

From the question, we can infer that the ratio of the mountain height to the surveyor's horizontal distance from the mountain is equal to the tangent of 35 degrees - the mountain height is the "opposite side", while the horizontal distance is the "adjacent side". In other words:

$tan (35^{\circ}) = \frac{mountain\ height}{ 2400\ ft}$

Solving for the mountain height gives a vertical distance of 1680.5 feet.

Report an Error

View Trigonometry Tutors

Mohammad Talha
Certified Tutor

University of Toronto, Mississauga, Bachelor, Chemistry, and Environmental Science.

View Trigonometry Tutors

Joseph
Certified Tutor

Rutgers University-New Brunswick, Bachelor in Arts, Chemistry. Rutgers Graduate School of Biomedical Sciences, Current Grad S...

View Trigonometry Tutors

Vaishnavi
Certified Tutor

SRM University, Bachelor of Technology, Aerospace Engineering. University of Petroleum and Energy Studies, Masters in Busines...

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Trigonometry Tutors in Top Cities:

Popular Courses & Classes

LSAT Courses & Classes in New York City, GRE Courses & Classes in San Diego, SAT Courses & Classes in Los Angeles, SAT Courses & Classes in Miami, GMAT Courses & Classes in Houston, ACT Courses & Classes in Washington DC, Spanish Courses & Classes in Atlanta, ACT Courses & Classes in Atlanta, ISEE Courses & Classes in Seattle, Spanish Courses & Classes in Washington DC

Popular Test Prep

LSAT Test Prep in Atlanta, GRE Test Prep in Los Angeles, ISEE Test Prep in New York City, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Houston, MCAT Test Prep in San Diego, LSAT Test Prep in Seattle, ACT Test Prep in Washington DC, GMAT Test Prep in Miami

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Trigonometry : Solving Triangles

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Finding Angles

Example Question #1 : Finding Angles

Example Question #2 : Finding Angles

Example Question #3 : Finding Angles

Example Question #2 : Finding Angles

Example Question #1 : Solving Triangles

Example Question #367 : Trigonometry

Example Question #368 : Trigonometry

Example Question #1 : Finding Sides

Example Question #2 : Finding Sides

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: