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ACT Math : How to find positive tangent

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Example Questions

Example Question #22 : Trigonometry

Math2

For triangle $\DeltaABC$ $\Delta ABC$ , what is the cotangent of angle $\angle B$ ?

Possible Answers:

$\frac{f}{d}$

$\frac{f}{e}$

$\frac{d}{f}$

$\frac{d}{e}$

Correct answer:

$\frac{f}{d}$

Explanation:

The cotangent of the angle of a triangle is the adjacent side over the opposite side. The answer is $\frac{f}{d}$

Math2-p1

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Example Question #1 : How To Find Positive Tangent

What is the tangent of the angle formed between the origin and the point (-12,-5) if that angle is formed with one side of the angle beginning on the -axis and then rotating counter-clockwise to ? Round to the nearest hundredth.

Possible Answers:

0.42

0.38

2.4

-2.4

-0.42

Correct answer:

0.42

Explanation:

Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the -axis as your reference point for your angle. (Hence, it is called the "reference angle.")

Now, it is easiest to think of this like you are drawing a little triangle in the third quadrant of the Cartesian plane. It would look like:

Tan125

So, the tangent of an angle is:

$\frac{opposite}{adjacent}$ or, for your data, $\frac{5}{12}$ .

This is 0.41666666666667 . Rounding, this is 0.42 . Since (-12,-5) is in the third quadrant, your value must be positive, as the tangent function is positive in that quadrant.

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Example Question #3 : How To Find Positive Tangent

What is the tangent of the angle formed between the origin and the point (-5,-16) if that angle is formed with one side of the angle beginning on the -axis and then rotating counter-clockwise to ? Round to the nearest hundredth.

Possible Answers:

3.2

0.31

-3.2

5.14

-0.31

Correct answer:

3.2

Explanation:

Recall that when you calculate a trigonometric function for an obtuse angle like this, you always use the -axis as your reference point for your angle. (Hence, it is called the "reference angle.")

Now, it is easiest to think of this like you are drawing a little triangle in the third quadrant of the Cartesian plane. It would look like:

Tan516

So, the tangent of an angle is:

$\frac{opposite}{adjacent}$ or, for your data, $\frac{16}{5}$ , or 3.2 . Since (-5,-16) is in the third quadrant, your value must be positive, as the tangent function is positive in this quadrant.

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Example Question #2 : How To Find Positive Tangent

A ramp is being built at an angle of $30^{\circ}$ from the ground. It must cover horizontal feet. What is the length of the ramp? Round to the nearest hundredth of a foot.

Possible Answers:

$12.41\:ft$

$16.91\:ft$

$13.53\:ft$

$5.77\:ft$

$11.55\:ft$

Correct answer:

$11.55\:ft$

Explanation:

Based on our information, we can draw this little triangle:

Tan10

Since we know that the tangent of an angle is $\frac{opposite}{adjacent}$ , we can say:

$tan(30)=\frac{y}{10}$

This can be solved using your calculator:

y=10tan(30) or 5.77350269189626

Now, to solve for , use the Pythagorean Theorem, a^2+b^2=c^2 , where and are the legs of a triangle and is the triangle's hypotenuse. Here, c=r , so we can substitute that in and rearrange the equation to solve for :

$r=\sqrt{a^2+b^2}$

Substituting in the known values:

$r=\sqrt{10^2+5.77350269189626^2}$ , or approximately 11.54700538379252 . Rounding, this is 11.55 .

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ACT Math : How to find positive tangent

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #22 : Trigonometry

Example Question #1 : How To Find Positive Tangent

Example Question #3 : How To Find Positive Tangent

Example Question #2 : How To Find Positive Tangent

All ACT Math Resources

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