Answer:
The height of the blimp above the ground = 1635.363039 feet.
Step-by-step 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.
