Question

Solve the right triangle. 34.5 Find the length of the side opposite to the given angle. (Round your answer to two decimal places.) Find the length of the side adjacent to the given angle. (Round your answer to two decimal places.) Find the other acute angle. rad

Answer 1

Answer:

a) 388.03

b) 148.49

c) π/8

Step-by-step explanation:

Find the diagram attached

Let the opposite side be y

Given

a) Hypotenuse = 420

theta = 3π/8 rad

theta = 3(180)/8

theta = 67.5degrees

Using the SOH CAH TOA identity

sin theta = opposite/hypotenuse

sin 67.5 = y/420

x = 420sin67.5

x = 420(0.9238)

x = 388.03

Hence the length of the side opposite to the given angle is 388.03

b) Hypotenuse = 420

theta = 3π/8 rad

theta = 3(180)/8

theta = 67.5degrees

Using the SOH CAH TOA identity

cos theta = adjacent/hypotenuse

cos 67.5 = x/420

x = 420cos67.5

x = 420(0.3827)

x = 148.49

Hence the length of the side adjacent to the given angle is 148.49

c) The sum of angle in the triangle is π

Let the measure of the unknown angle be z

z + 3π/8 + π/2 = π

z + 3π+4π/8 = π

z + 7π/8 = π

z = π - 7π/8

z = (8π-7π)/8

z = π/8

Hence the measure of the other acute angle is π/8