Question

1. a large monument with height of 2351 m is located exactly halfway between points k and l. michael is standing at point m and finds that he is 14.2 km from l and 17.1 km from k. he also measures the angle between k and l to be 47°. determine the angle of elevation to the top of the monument, measured from point m. 7t

Explanation:

Step1: Convert units

Since \(17.1\mathrm{km} = 17100\mathrm{m}\), \(14.2\mathrm{km}=14200\mathrm{m}\).

Step2: Use the tangent function

In the right - triangle, \(\tan x=\frac{2351}{14200}\) (opposite side over adjacent side in the right - triangle formed by the monument height and the distance from \(M\) to the base of the line of sight).

Step3: Calculate the angle

\(x = \arctan(\frac{2351}{14200})\)
Using a calculator, \(\frac{2351}{14200}\approx0.16556\)
\(x=\arctan(0.16556)\approx9.4^{\circ}\)

Answer:

The angle of elevation \(x\) is approximately \(9.4^{\circ}\)