Answer:
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)
