Please help! Need to draw pic

Question

Elsa and Anna are standing 150 feet apart on flat ground looking at a tower. The angle ° 56 of depression from the top of the tower to Elsa’s feet is . The angle of depression from ° 75 the top of the tower to Anna’s feet is . How tall is the tower, and how far is the top of the tower from each girl’s feet?

Answer 1

You must draw a picture:

tower top, Elsa on right of tower, Anna on left of tower; label then points T, E, and A.

then angle TEA is 56 and TAE is 75.

h is the height of the tower, and Anna is x feet away from the base of the tower.

tan 75 = h/x ----> x = h/tan 75

tan 56 = h/(150-x) ----> 150-x = h/tan56

adding them together... left side is 150...

h factors out of the right side

150 = h( cot 75 + cot 56) <--- cot t = 1/tan t

h = 159.158335195348635715012-

then

x = h/x = 42.6463474-

so then 150 - x = 116.51203

tower top to Elsa by pythagorean is 197.247122...