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a fire started at a campsite located 8 miles from the base of a mountain. if the angle of elevation from the fire to the top of the mountain is 14, how high is the mountain?

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Tan θ°= opposite/adjacent
Opposite is the side facing the angle given or angle we looking for so here the angle is 14°
Opposite is the height of the mountain which we are looking for (so let the unknown side be h)
Adjacent is the distance between the fire and the base of the mountain which is 8miles

So Tan 14°= opp/adj
Tan 14°= h/8miles
Cross multiply or multiple both sides by 8miles
8Tan14°= h
1.9946miles =h
But height is mostly measured in metres or feet especially for buildings or monuments
We convert 1.9946miles to metres
1miles = 1609.344metres
So 1.9946 miles to metres = 1.9946 x 1609.344
=3209.99754metres

The height of the mountain is 3209.9975metres
User Dasqueel
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