Question 1109680
A tree standing vertically on the side of the hill makes an angle of 115º with the side of the hill.
 At a point 68ft. down the slope, the tree subtends an angle of 22º.
 Find the height of the tree?
:
Draw this out, the tree top and bottom and a point 68' down the hill form a triangle tbp
Let t = the top of the tree, b = the bottom of the tree, p = point 68' down from the tree
angle t = 22 degrees
angle b = 115 degrees
therefore 180 - 22 - 115 = 43 degrees = angle p
bp = 68ft
let x = the height of the tree. Use the law of sines
{{{x/sin(43)}}} = {{{68/sin(22)}}}
find the sines
{{{x/.682}}} = {{{68/.3746}}}
cross multiply
.3746x = 68 * .682
x = {{{46.376/.3746}}}
x = 123.8 ft is the height of the tree