If the shadow of a tree increases by 3 meters when the angle of elevation of the sun’s rays decreases from 65°to 50°, find the height of the tree

Answer 1

make a sketch, label the position of the 50° angle as A
label the position of the 65° angle as B, where B is
clearly closer to the tree , The AB = 3 metres

label the top of tree as P and its bottom as Q
since angle PBQ = 65, angle ABP = 112°, which makes angle APB = 15°

by the sine law:
PB/sin50 = 3/sin15
PB = 3sin50/sin15 = ....

Now triangle PBQ is right-angled, so
so sin 65 = PQ/PB
PQ = height of tree = PBsin65
= (3sin50/sin15)(sin65) = ......

Answer 2

Draw a diagram and review your basic trig functions. If the height is h, then
h cot50° - h cot65° = 3