Solve the right triangle. State the side lengths to the nearest tenth and the angle measures to the nearest degree.

Question

asked Nov 3, 2020 34.8k views

2 Answers

Ostas · Answer 1 · 2020-11-08T05:26:23+0000

Answer:

Option B

Explanation:

The two acute angles of a right triangle are equal.

$\angle \: A + 18 = 180$

$\angle \: A= 90 - 18 = 72 \degree$

Recall the mnemonics SOH-CAH-TOA

The tangent ratio is opposite over adjacent.

$\tan(18) = (AC)/(21)$

$AC = 21 \tan(18)$

AC = 6.8

The sine ratio is opposite over hypotenuse

Using the sine ratio,

$\sin(72) = (21)/(AB)$

$AB = (21)/( \sin(72) ) = 22.1$