Unit 2 test: Right Triangle Trigonometry

Use the triangle below. Find $\sin A$.

In the same triangle ($AC = 24$, $BC = 7$, $AB = 25$, right angle at $C$), find $\cot A$.

$\theta$ is an acute angle with $\tan\theta = \dfrac{8}{15}$. Find $\csc\theta$.

Which expression is equal to $\cos 71^\circ$?

Find $x$ if $\sin(4x)^\circ = \cos(2x + 30)^\circ$, where both angles are acute.

The hypotenuse of a $45^\circ$-$45^\circ$-$90^\circ$ triangle is $9\sqrt{2}$. How long is each leg?

The short leg of a $30^\circ$-$60^\circ$-$90^\circ$ triangle is $5$. What is the exact length of the long leg?

Find the exact value of $\tan 30^\circ$, with a rational denominator.

Find the exact value of $\cos^2 30^\circ - \sin^2 30^\circ$.

A right triangle has a $27^\circ$ angle and a hypotenuse of $18$. Find the length of the leg opposite the $27^\circ$ angle, to the nearest tenth.

In right triangle $ABC$, $\angle C = 90^\circ$, $\angle A = 38^\circ$ and $AC = 11$. Find the hypotenuse $AB$, to the nearest tenth.

The legs of a right triangle are $9$ and $4$. Find the measure of the angle opposite the leg of length $9$, to the nearest tenth of a degree.

In right triangle $ABC$, $\angle C = 90^\circ$, $\angle B = 64^\circ$ and $BC = 12$. Which equation can be used to find $AC$?

You stand on level ground $35$ m from the base of a tree. The angle of elevation to the top of the tree is $41^\circ$. How tall is the tree, to the nearest tenth of a meter? (Treat your eye as being at ground level.)

From the top of a $200$ ft cliff, the angle of depression to a boat is $23^\circ$. How far is the boat from the base of the cliff, to the nearest tenth of a foot?