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.

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \(KL^{2}=MK^{2}+ML^{2}-2(MK)(ML)\cos\angle KML\).
Let \(MK = 17.1\space km=17100\space m\), \(ML = 14.2\space km = 14200\space m\), \(\angle KML=47^{\circ}\).

$$
LATEXBLOCK0
$$

Since the monument is halfway between \(K\) and \(L\), the horizontal distance from \(M\) to the monument \(d=\frac{KL}{2}\approx2018.785\space m\)

Step2: Use the tangent function

The tangent of the angle of elevation \(x\) is \(\tan x=\frac{h}{d}\), where \(h = 2351\space m\) and \(d\approx2018.785\space m\)

$$ \tan x=\frac{2351}{2018.785}\approx1.1645 $$

$$ x=\arctan(1.1645)\approx49.4^{\circ} $$

Answer:

The angle of elevation is approximately \(49.4^{\circ}\)