Question

A tree on a hillside casts a shadow c = 230 ft down the hill. if the angle of inclination of the hillside is b = 19° to the horizontal and the angle of elevation of the sun is a = 49°, find the height of the tree. (round your answer to the nearest foot.)

Answer 1

From a point A draw a line 19° to the horizontal representing the hill. On the hill, 230 ft from the point A, draw a vertical line.h, representing the height of the tree. From the point A, draw another line 49° to the horizontal to the top of the tree. Lastly, from the bottom of the tree, extend a vertical line (y) down to a point on the horizontal.
let x be the distance from point A to when y intersects the horizonal.
x/230=cos 19
x=230 cos 19=217.5

y/x=tan 19
y=xtan19
y=217.5 tan 19=74.88
(h+y)/x=tan 49
h+y=xtan 49=217.5tan49=250.205 
hence
h=250.205-74.88=175.325 ft

the answer is:
height of the tree ~ 175 ft