Unit 9 test: Right Triangles and Trigonometry

A right triangle has legs $7$ and $24$. How long is the hypotenuse?

A triangle has sides $10$, $12$ and $15$. How should it be classified?

The hypotenuse of a 45°-45°-90° triangle is $9$. Find the exact length of a leg. (Type a square root as sqrt(…).)

The short leg of a 30°-60°-90° triangle is $5$. Find the exact length of the long leg.

In right triangle $ABC$, the right angle is at $C$, $BC = 9$ and $AC = 40$. Find $\tan A$ as a fraction.

In a right triangle, the leg adjacent to a $33^\circ$ angle is $15$. Find the leg opposite the $33^\circ$ angle, to the nearest tenth.

$A$ is an acute angle with $\sin A = \dfrac{12}{13}$. Find $\cos A$ as a fraction.

A right triangle has a hypotenuse of $30$ and an acute angle of $25^\circ$. Find the leg opposite the $25^\circ$ angle, to the nearest tenth.

Find the acute angle $x$, in degrees, if $\sin x = \cos 17^\circ$.

A right triangle has legs $10$ and $7$. Find the angle opposite the leg of length $10$, to the nearest tenth of a degree.

A kite is flying at the end of a straight $60$-meter string. The kite is $42$ meters above the ground (ignore the height of the person holding the string). What is the angle of elevation of the string, to the nearest tenth of a degree?

In triangle $ABC$, $A = 42^\circ$, $B = 77^\circ$ and $a = 15$. Find $b$ to the nearest tenth.

In triangle $ABC$, $A = 35^\circ$, $a = 8$ and $b = 12$. How many different triangles fit this information?

In triangle $ABC$, $a = 9$, $b = 12$ and $C = 110^\circ$. Find $c$ to the nearest tenth.

A triangle has sides $5$, $6$ and $10$. Find its largest angle, to the nearest tenth of a degree.