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A surveyor measures the angle of elevation of the top of a mountain from a point at
sea level as 20â—¦. She then travels 1000 m along a road that slopes uniformly uphill
towards the mountain. From this point, which is 100 m above sea level, she measures
the angle of elevation as 23â—¦. Find the height of the mountain above sea level, correct to
the nearest metre.
(use sin rule/ cos rule)

Respuesta :

xero099

The height of the mountain from a point a sea level is approximately 1496.650 meters.

What is the height of mountain from sea level?

First, we construct the geometric diagram of the situation and find all needed angles and sides to determine the height of the mountain. First, we determine the missing side x by the law of sines:

Law of sines

1000 m/sin 3° = x/sin 14.261°

x ≈ 4706.886 m

Now we determine the height of the mountain by trigonometric functions:

h = 100 m + (4706.886 m) · sin 17.261°

h ≈ 1496.650 m

The height of the mountain from a point a sea level is approximately 1496.650 meters.

To learn more on law of sines: https://brainly.com/question/13098194

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