Question

Archie and Veronic are located one mile (5280 ft) apart on the ground. They observe a blimp directly over the road between them. Archie measures the angle of elevation from the ground to the blimp to be 53 degrees. Veronica measures the angle of elevation from the ground to the blimp to be 22 degrees. How far above the ground is the blimp?

Answer 1

The height of the blimp above the ground = 1635.363039 feet.

Explanation:

Archie and Veronica are located one mile (5280 ft) apart on the ground. So AV = 5280 feet.

Suppose the height of blimp above the ground is XB = h feet.

Archie measures the angle of elevation from the ground to the blimp to be 53 degrees. So angle ∠BAX = 53°.

Veronica measures the angle of elevation from the ground to the blimp to be 22 degrees. So angle ∠BVX = 22°.

Considering Right triangle ΔAXB, cot(A) = AX / XB

AX = XB*cot(A) = h*cot(53°) = 0.75355405*h

Considering Right triangle ΔVXB, cot(B) = VX / XB

VX = XB*cot(B) = h*cot(22°) = 2.475086853*h

We know AV = 5280 and AX + VX = AV.

So AX + VX = 5280.

0.75355405*h + 2.475086853*h = 5280.

3.228640904*h = 5280.

h = 5280 / 3.228640904 = 1635.363039 feet.

Hence, the height of the blimp above the ground = 1635.363039 feet.