Question

If the tree grows an additional 10 feet, what is the new angle of

elevation from the point 25 feet from the base of the tree to the top of the tree?

A) 42.30
B) 47.1°
C) 49.8°
D) 54.6

Answer 1

B) 47.1°

Explanation:

The tangent relation is useful here.

Tan = Opposite/Adjacent

The original height of the tree is the side of the triangle that is opposite the angle of elevation:

Opposite = Adjacent × Tan

original height = (25 ft)×tan(34°) ≈ 16.863 ft

__

After growing an additional 10 ft, the tree has a height of ...

16.863 ft + 10 ft = 26.863 ft

Then the angle of elevation is found from ...

tan(angle) = (26.863 ft)/(25 ft) ≈ 1.07451

angle of elevation = arctan(1.07451) ≈ 47.057°

The angle of elevation to the top of the tree is about 47.1°.