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18 days ago

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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?

1 answer:

Inessa [9K]18 days ago

3 0

Answer:

The blimp's altitude is 1635.363039 feet above the ground.

Step-by-step explanation:

Archie and Veronica stand one mile (5280 ft) apart on the ground, leading to AV = 5280 feet.

Let's denote the blimp's height above ground as XB = h feet.

Archie records the angle of elevation from the ground to the blimp as 53 degrees, signifying angle ∠BAX = 53°.

Veronica, meanwhile, measures the angle of elevation to the blimp at 22 degrees, indicating angle ∠BVX = 22°.

In Right triangle ΔAXB, we utilize cot(A) = AX / XB.

Thus, AX can be expressed as AX = XB*cot(A) = h*cot(53°) = 0.75355405*h.

In Right triangle ΔVXB, cot(B) is similar: cot(B) = VX / XB.

Consequently, VX is VX = XB*cot(B) = h*cot(22°) = 2.475086853*h.

We know AV = 5280, meaning AX + VX = AV.

Therefore, AX + VX equals 5280.

From here, we can write: 0.75355405*h + 2.475086853*h = 5280.

This simplifies to: 3.228640904*h = 5280.

Thus, h is calculated as 5280 / 3.228640904 = 1635.363039 feet.

Thus, the blimp's height from the ground is 1635.363039 feet.

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