4. A tree stands vertically on top of a hill whose angle of inclination is 30°. The top and base of the tree are 4√3 and 4 meters, respectively, from a point P at the foot of the hill. What is the angle of subtended by the tree at point P?

Answer 1

Did you make a sketch?

On mine I let the top of the tree be A and its bottom be B
look at triangle APB.
angle ABP = 120° , AP = 4√3, BP = 4

by the sine law:
sinA/4 = sin120/4√3
sinA = 4(√3/2)/(4√3) = .5
A = 30°
so angle APB = 180-120-30 = 30°