Answer:
B) 47.1°
Step-by-step 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
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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°.
