Question

mcr3u
trigonometry assignment t /29

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
2351 m
14.2 km
17.1 km

Explanation:

Step1: Convert units

Since \(1\space km = 1000\space m\), then \(2351\space m=2.351\space km\).

Step2: Use the Law of Cosines

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

$$
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Since the monument is halfway between \(K\) and \(L\), the horizontal distance from \(M\) to the monument \(d=\frac{KL}{2}\approx6.36\space km\)

Step3: Use the tangent function

The tangent of the angle of elevation \(x\) is \(\tan x=\frac{\text{height}}{\text{horizontal distance}}\). Here, height \(h = 2.351\space km\) and horizontal distance \(d = 6.36\space km\)

$$ \tan x=\frac{2.351}{6.36}\approx0.37 $$

$$ x=\arctan(0.37)\approx20.3^{\circ} $$

Answer:

The angle of elevation is approximately \(20.3^{\circ}\)