Question

Using the diagram below, solve the right triangle. Round angle measures to the

nearest degree and segment lengths to the nearest tenth.
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Answer 1

m∠A = 17 degrees m∠B = 73 degrees m∠C = 90 (given) a = 12 (given) b = 40 c = 42 (given)

Explanation:

Use sin to solve m∠A

sin x = 12/42 Simplify

sin x = 0.2857 Use the negative sin to solve for x

sin^-1 x = 17 degrees

Add together all of the angle measures to solve for m∠B

17 + 90 + x = 180 Add

107 + x = 180

-107 -107

x = 73 degrees

Use Pythagorean Theorem to solve for b

12^2 + x^2 = 42^2 Simplify

144 + x^2 = 1764

-144 -144

x^2 = 1620 Take the square root of both sides

x = 40