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

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

Step-by-step 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)