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Use the information in the illustration to find the distance from the boathouse to the cabin. Round your answer to the nearest yard.

User Vesperae
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1 Answer

5 votes

Answer:

The distance from the boathouse to the cabin = 50 yd (nearest yard)

Explanation:

The question is incomplete.

Question:

To find the distance from the

boathouse on shore to the cabin on the island, a surveyor measures from the boathouse to point X as shown. He then finds m∠X with an instrument called a transit. Use the surveyor’s

measurements to find the distance from the boathouse to the cabin.

Find attached the diagram of the question.

Solution:

Let the distance from the boathouse to the cabin = y

the distance from the boathouse to the point X = 30yard

Find attached the diagram for the solution.

From the diagram, the triangle is a right angled triangle

Opposite = y

Adjacent = 30yd

∠X = 59°

Using trigonometry (SohCahToa)

We would apply Toa since adjacent is given and we are looking for opposite

tan θ = opposite/adjacent

tan 59° = y/30

y = 30 tan 59

y = 30(1.6643)

y = 49.929

y = 50 yd (nearest yard)

The distance from the boathouse to the cabin = 50 yd (nearest yard)

Use the information in the illustration to find the distance from the boathouse to-example-1
Use the information in the illustration to find the distance from the boathouse to-example-2
User Bhushan B
by
3.4k points