Question

Solve ARST.
R
S
72°
7
T
15
r
S

Answer 1

• r = 14.3
• s = 4.6
• S = 18°

Explanation:

You want the solution to right triangle RST with RS = 15, R = 72°, T = 90°.

Trig relations

The mnemonic SOH CAH TOA reminds you ...

Sin = Opposite/Hypotenuse ⇒ r = 15·sin(72°) ≈ 14.3

Cos = Adjacent/Hypotenuse ⇒ s = 15·cos(72°) ≈ 4.6

The acute angles in a right triangle are complementary, so ...

S = 90° -R = 90° -72° = 18°