Question

trig mixed practice
5 of 9
desmos graphing calculator texas version
find the measure angle indicated with a \?\ on each triangle. round your answer to the nearest degree. enter numbers only, no symbols or words.
(a)
(b)
(c)

Explanation:

Step1: Solve for angle (a)

We have a right triangle with adjacent side to the unknown angle: $13\cos(20^\circ)$, opposite side: $13\sin(20^\circ)$. Use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(?)=\frac{13\sin(20^\circ)}{13\cos(20^\circ)}=\tan(20^\circ)$? No, wait: the given angle is $20^\circ$, hypotenuse 13. The unknown angle is complementary: $90^\circ-20^\circ=70^\circ$.

Step2: Solve for angle (b)

Right triangle, adjacent=12, hypotenuse=24. Use $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos(?)=\frac{12}{24}=0.5$, so $?=\arccos(0.5)=60^\circ$

Step3: Solve for angle (c)

Right triangle, opposite=9, adjacent=21. Use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(?)=\frac{9}{21}\approx0.4286$, so $?=\arctan(0.4286)\approx23^\circ$

Answer:

(a) 70
(b) 60
(c) 23