In AFGH, FH = 8ft FG = 13H and m angle F = 72' , Find the length of HG. Label the diagram to help you. Round your answer to the nearest whole number
Hg=?
Answer 13 ft
We can start by labelling the diagram with the given information:
- AFGH is a parallelogram
- FH = 8ft
- FG = 13ft
- m angle F = 72 degrees
Now, let's find the length of GH by using the law of cosines.
The law of cosines is a formula that relates the lengths of the sides of a triangle to the cosine of one of its angles:
c² = a² + b² - 2ab * cos(C)
In our case:
- a = FH = 8 ft (base of the triangle)
- b = FG = 13 ft (the diagonal of the parallelogram)
- C = angle F = 72° (angle between the base and the diagonal)
Our goal is to find c - the length of HG.
(1) c² = 8² + 13² - 2*8*13*cos(72°)
First, we calculate the square of each side and the cosine of the angle:
8² = 64
13² = 169
cos(72°) = 0.3090
Now we can substitute the values back into equation (1):
(2) c² = 64 + 169 - 2*8*13*0.3090
Calculate the value inside the parenthesis:
2*8*13*0.3090 = 64.9696
Substitute back into equation (2):
(3) c² = 64 + 169 - 64.9696
c² = 168.0304
Now, take the square root of both sides:
c = √168.0304
c ≈ 12.97
Round to the nearest whole number:
c ≈ 13 ft
So the length of HG is approximately 13 ft.