Trig help, please!?

Question

Ahmad and Bob want to calculate the height of a tree. They measure the angles of elevation to the top of the tree. The angle of elevation from Bob, who is standing 60 m from the base of the tree, to the top of the tree, is 40˚. The angle of elevation from Ahmad, who is standing 80 m from Bob, is 50˚.

Calculate the height of the tree.

Answer 1

sohcahtoa

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

You have the adjacent value (60m) and the value of the angle (40) and you want to find the opposite value (tree height).

tan(40) = x/60

x = 60*tan(40) = 50.34m

Answer 2

First, you only need Bob's measurements. You can disregard Ahmad.

In this problem you could use the "tan" formula

The base line is 60 metres (from the base of the tree to Bob)
then imagine the tree at the end of the line as a vertical line
from the opposite side is the angle of 40 degrees going to the top of the tree

The tangent formula is: tan of angle = opposite side divided by the adjacent side

= tan of 40 = .8390996

.8390996 = a/b

.8390996 = a/60


a = 60 x .8390996 = 50.35 metres high

Answer 3

Tangent is opposite over adjacent.

In other words, the height of the tree is:

tan (40) = h/60
h = 60 * tan(40)
h= 50.5 m.

Ahmad's distance from the tree must be:
tan(50) = 50.5/d
d = 50.5/tan(50)
d = 19.8 m

The numbers are all obviously rounded off (this makes since - you started out with 2 significant digits, so your answer should be rounded off to 2 significant digits), since the distance between the two can't be greater than the sum of their distance from tree. There's no reason to assume the tree, Bob, and Ahmad lie in a straight line, but, in this case, they must. Bob is on one side of the tree and Ahmad is on the other.

Answer 4

tanA=p/b
p=b*tanA
for Bob p=60tan40 p=50.34m
for Ahmad p=140tan50 p=166.8m

Answer 5

I don't know why you need Ahmad's measurements for this.

Just take X = dist_Bob * tan(angle_Bob) = 50.34 m

Answer 6

21.75m