Question

Question in picture ​

Answer 1

Answers:

cos(A) = 0.8480

tan(B) = 1.6

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Explanation:

Before we can compute cos(A), we'll need to find the hypotenuse.

Use the pythagorean theorem.

a^2 + b^2 = c^2

8^2 + 5^2 = c^2

89 = c^2

c^2 = 89

c = sqrt(89)

The hypotenuse is exactly sqrt(89) units long.

This will allow us to find the cos(A) value

cos(angle) = adjacent/hypotenuse

cos(A) = AC/AB

cos(A) = 8/sqrt(89)

cos(A) = 0.84799830400509 which is approximate

cos(A) = 0.8480 when rounding to four decimal places

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For the tangent ratio, we won't use the hypotenuse. Instead, we use the opposite and adjacent sides like so:

tan(angle) = opposite/adjacent

tan(B) = AC/BC

tan(B) = 8/5

tan(B) = 1.6