Posted by Rutba on .
A 5.0 m tree is leaning 5° from the vertical. To prevent it from leaning any farther, a stake needs to be fastened 2 m from the top of the tree at an angle of 60°with the ground. How far from the base of the tree, to the nearest metre, must the stake be?

Math 
Reiny,
I visualize a triangle ABC such that
AB = 3
angle B = 95°
angle C = 60° , so angle A = 1809560 = 25°
BC = x, our required length
By the sine law:
x/sin25 = 3/sin60
x = 3sin25/sin60 = appr 1.46 m