Question

A water tower 30 m tall is located at the top of a hill. From a distance of D = 120 m down the hill it is observed that the angle formed between the top and base of the tower is 8°. Find the angle of inclination of the hill

Answer 1

about 48°

Explanation:

You want the angle of inclination of a hill with a 30 m water tower on top that subtends an arc of 8° when observed from a point 120 m down the hill.

Law of sines

We have triangle ABD with sides AB and AD given, along with angle D. This is sufficient information to let us find the measure of angle B using the Law of Sines.

sin(B)/AD = sin(D)/AB

B = arcsin(AD/AB·sin(D))

B = arcsin(120/30·sin(8°) ≈ 33.83°

Inclination

Angle BDE is the complement of this angle, so is 56.17°. Angle ADE is 8° less, so is ...

∠ADE = ∠BDE -8° = 56.17° -8° = 48.17°

The angle of inclination of the hill is about 48.17°.

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