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 \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 14.2\), \(b=17.1\), and \(C = 47^{\circ}\). First, find the distance \(d\) from \(M\) to the base of the monument (since the monument is halfway between \(K\) and \(L\)).

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Step2: Use the tangent function

The tangent of the angle of elevation \(x\) is given by \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side is the height of the monument (\(h = 2351\space m\)) and the adjacent side is \(d\approx12760\space m\).

$$ \tan x=\frac{2351}{12760}\approx0.1842 $$

$$ x=\arctan(0.1842)\approx 10.4^{\circ} $$

Answer:

The angle of elevation is approximately \(10.4^{\circ}\)