Question

In triangle ABC, angles A and angle B are complementary, where cos A = 0.5.

What is the measure, in degrees, of angle B?

Hint: first find cos^-1 (.5), then find the complement of this angle.

60 degrees

30 degrees

90 degrees

0 degrees

Answer 1

Answer:

∴∠B=30°

Step-by-step explanation:

Complementary:

Two angles is said to complementary when the sum of two angles is 90 degree.

Given that,

∠A and ∠B are complementary.

Then,  ∠A + ∠B = 90°

Cos A = 0.5

$\Rightarrow A=cos^{-1}(0.5)$

$\Rightarrow A=cos^{-1}(cos \ 60^\circ)$

$\Rightarrow A=60^\circ$

Since

 ∠A + ∠B = 90°

⇒ 60°+ ∠B = 90°      [ plug ∠A= 60°]

⇒∠B=90°-60°

⇒∠B=30°

∴∠B=30°