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: Use the Law of Cosines to find the distance between \(K\) and \(L\)

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Let \(a = 14.2\), \(b = 17.1\), and \(C=47^{\circ}\).

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Since the monument is halfway between \(K\) and \(L\), the horizontal distance from the monument to \(M\) is \(d=\frac{12.8}{2}=6.4\mathrm{km}=6400\mathrm{m}\)

Step2: Use the tangent function to find the angle of elevation \(x\)

The tangent function is \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side is the height of the monument (\(h = 2351\mathrm{m}\)) and the adjacent side is \(d = 6400\mathrm{m}\).

$$ \tan x=\frac{2351}{6400}\approx0.367 $$

$$ x=\arctan(0.367)\approx20.1^{\circ} $$

Answer:

The angle of elevation \(x\) is approximately \(20.1^{\circ}\)