Answer:
about 48°
Step-by-step 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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