Using the diagram below, solve the right triangle. Round angle measures to the nearest degree and segment lengths to the nearest tenth.

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

Step-by-step 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

step-by-step explanation: