A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29° From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 34° How high (in feet) is the mountain?

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the mountain is 3110.5767 feet.

What is Tangent (Tanθ)?

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The height of the mountain from the first point,

[tex]\tan(29^o) = \dfrac{H}{x+1000}\\\\H = (1000+x) \times \tan(29^o)[/tex]

The height of the mountain from the second point,

[tex]\tan(34^o) = \dfrac{H}{x}\\\\H = x \times \tan(34^o)[/tex]

Equating the height,

H = H

(1000+x) × tan(29°) = x tan( 34°)

x = 4611.5767 feet

Now, the height of the mountain is,

H = x tan(34°)

H = 3110.54776 feet

Hence, the height of the mountain is 3110.5767 feet.

Learn more about Tangent (Tanθ):

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