Question

A lodge stands 45 ft tall on the shore of a lake. From a point on the opposite shore,

the angle of elevation to the top of the lodge is 6º. Approximately, how wide is the
lake?
428 ft
O 45 ft
431 ft
322 ft

Answer 1

To determine the lake's width, the tangent of the angle of elevation, which is 6º, is applied. After calculating, you find that the width of the lake is approximately 428 ft.

Step-by-step explanation:

To find the width of the lake when given the height of the lodge and the angle of elevation, you can use trigonometry. The lodge's height is the opposite side of the right triangle formed, and the lake's width is the adjacent side you want to find. The angle of elevation is 6º. To solve for the width of the lake (let's call it x), you would use the tangent function:

tan(angle) = opposite/adjacent

tan(6º) = 45 ft / x

Rearrange the equation to solve for x:

x = 45 ft / tan(6º)

Use a calculator to find tan(6º):

tan(6º) ≈ 0.1051

Substituting back into the equation,

x = 45 ft / 0.1051 ≈ 428 ft

Therefore, the approximate width of the lake is 428 ft.