Question

A roof has the shape of an isosceles triangle with equal sides 6 m long and base 10 m long. What is the measure of the angle of inclination of the roof to the nearest degree?

Answer 1

Answer:

33.56°

Step-by-step explanation:

First, we can draw this out. Looking at the picture, we are trying to find x, or the angle between the sides of lengths 10m and 6m.

We can solve this by applying the law of Cosines for one side of length 6m, as its corresponding angle (the one opposite the side) is the one we want to solve for:

c² = a² + b² - 2ab * cos(c)

6² = 6² + 10² - 2(6)(10)(cos(c))

subtract 6² from both sides to simplify

0 = 10² - 2(6)(10)(cos(c))

  = 100 - 120cos(c)

add 120cos(c) to both sides to isolate the variable and its coefficient

120cos(c) = 100

divide both sides by 120 to isolate the variable

cos(c) = 100/120 = 5/6

c = arccos(5/6) ≈ 33.56°