Question

A surveyor took the following measurements of two houses on opposite sides of a river. Based on these measurements, what is the distance between the two houses to the nearest foot?

A. 65 ft
B. 94 ft
C. 130 ft
D. 95 ft

Answer 1

To find the distance between the two houses, we can use the concept of trigonometry and the given information.

Step-by-step explanation:

To find the distance between the two houses, we can use the concept of trigonometry and the given information. The surveyor walked 100 m along the river to establish a baseline, and the angle from the baseline to the tree on the opposite bank is 35°. We can use the trigonometric function tangent to find the width of the river.

Tangent = Opposite/Adjacent

Let x be the width of the river. Using the trigonometric function tangent, we have:

Tan(35°) = x/100m

Simplifying this equation, we get:

x = 100m * Tan(35°)

x ≈ 57.4m

Converting this to feet, we have:

x ≈ 189ft

Therefore, the closest foot measurement of the distance between the two houses is approximately 189 ft.