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 o…

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asked Apr 10, 2021 137k views

1 Answer

Reuel · Answer 1 · 2021-04-14T14:22:14+0000

Answer:

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°