Question

A tree broke 14 ft. above the ground. The top of the tree now touches the level ground and the trunk is still partially attached to the stump. The angle of inclination of the tree is 43°. To the nearest foot, determine the height of the tree before it broke.

Answer 1

Draw a right triangle ABC with, the point where the top touches the ground and one leg, BC, the stump, measuring 14 ft.
The height of the tree = hypotenuse + stump BC (14 ft)
If the ∠ of inclination = 43°, then ∠ CAB = 37°
Now let's apply the law of sine:
sin 37°/14 = sin 43°/AB  →and AB = 14.sin 43°/sin 37° = 15.86
Hypotenise² = AB² + CB²
Hypotenuse² = 15.85² + 14²  = 447.22 → and Hypotenuse =  21.14 ft
Tree Height = hypotenuse + stump = 21.14 + 14 ≈ 35 ft