Question

A surveyor identifies two points j and k on opposite sides of a valley. she then walks to a point a distance away from these points: point L. she measures the distance from j and L as 50 meters, the distance from k to L as 212 meters, and the measure of L as 57 degrees. what is the distance across the valley?

Answer 1

Explanation:

Let's call the distance across the valley "d". We can use the law of sines to solve for "d". The law of sines states that for any triangle with sides a, b, and c, and angles A, B, and C opposite those sides, the following equation holds:

a/sin(A) = b/sin(B) = c/sin(C)

In this case, we can set up the following equation:

50/sin(57) = 212/sin(180-57-d) = d/sin(57)

Simplifying this equation, we get:

d = (50*sin(57)*212)/sqrt(1-sin(57)^2) = 254.8 meters (rounded to one decimal place)

Therefore, the distance across the valley is approximately 254.8 meters.