Question

A farmer is estimating the surface area of his barn to find how much paint he needs to buy. One part of the barn is triangular as shown.

part a. The darkened sides in the figure are the edges of the roof. This trim will be painted white. Find the length of each of these two sides of the triangle. Explain how you found the answer.

part b. The triangular surface will be painted red. Find the area of the triangle. Explain how you found the answer

I have had to ask this question so many times because every time the answer was incomplete, someone was trying to get points, etc. Right now I need to understand how to do this question because my teacher won't explain how to do this to me. So please can someone actually answer this question and know what they are doing without giving me short answers that can't apply to the question? I really need help, please

Answer 1

PART A
By the sine law, we know that

sin(<A)/A is sin(<B)/B which is equal to sin(<C)/C.

THEREFORE,
sin(<120)/22m = sin(<30)/x

We need to isolate x.

x= 22m * (sin 30 degrees/sin 120 degrees)
x=12.7017059222m

Since we have an isosceles triangle, each side is about 12.7m.


PART B

We need to find the area of the triangle.

The formula for area is base x height /2 .

Our height we need to find out with the pythagorean theorem. half of our triangle means a length of the triangle at 11m.

a^2+b^2=c^2.

Therefore, (12.7)^2=11^2+x^2

Our height is 6.35084703891 m.

Base x height /2= area
area= 6.35084703891 m * 11 m / 2= 34.929658714m.

This is our area.