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Example Questions
Example Question #2 : Trigonometry
What is the ?
Example Question #3 : Trigonometry
In the right triangle above, which of the following expressions gives the length of y?
is defined as the ratio of the adjacent side to the hypotenuse, or in this case
. Solving for y gives the correct expression.
Example Question #1 : Arcsin, Arccos, Arctan
What is if
and
?
In order to find we need to utilize the given information in the problem. We are given the opposite and adjacent sides. We can then, by definition, find the
of
and its measure in degrees by utilizing the
function.
Now to find the measure of the angle using the function.
If you calculated the angle's measure to be then your calculator was set to radians and needs to be set on degrees.
Example Question #3 : Solving Triangles
If equals
and
is
, how long is
?
Not enough information to solve
This problem can be easily solved using trig identities. We are given the hypotenuse and
. We can then calculate side
using the
.
Rearrange to solve for .
If you calculated the side to equal then you utilized the
function rather than the
.
Example Question #4 : Solving Triangles
What is the length of CB?
Example Question #1 : Graphs And Inverses Of Trigonometric Functions
In this figure, angle . If side
and
, what is the value of angle
?
Undefined
For this problem, use the law of sines:
.
In this case, we have values that we can plug in:
Example Question #6 : Applying The Law Of Sines
In this figure, if angle
, side
, and side
, what is the value of angle
?
(NOTE: Figure not necessarily drawn to scale.)
Undefined
First, observe that this figure is clearly not drawn to scale. Now, we can solve using the law of sines:
.
In this case, we have values that we can plug in:
Example Question #71 : Trigonometry
In this figure, if angle , side
, and side
, what is the measure of angle
?
Undefined
Since , we know we are working with a right triangle.
That means that .
In this problem, that would be:
Plug in our given values:
Example Question #61 : Pre Calculus
In this figure, ,
, and
. What is the value of angle
?
Undefined
Notice that these sides fit the pattern of a 30:60:90 right triangle: .
In this case, .
Since angle is opposite
, it must be
.
Example Question #62 : Pre Calculus
A triangle has angles of . If the side opposite the
angle is
, what is the length of the side opposite
?
The pattern for is that the sides will be
.
If the side opposite is
, then the side opposite
will be
.
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