SOLUTION: Hey there Trina and mazaheer are standing on the same side of a red maple tree. The angle of elevation from mazaheer to the tree top is 67 degrees and the angle of elevation fr

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Question 1014440: Hey there
Trina and mazaheer are standing on the same side of a red maple tree. The angle of elevation from mazaheer to the tree top is 67 degrees and the angle of elevation from Trina to the tree top is 53°. If the tree is 12m high how far apart are the two girls? What is the distance between Trina and the top of the tree?
Can you please solve this step by step. I'm having a lot of trouble with this question. Thanks I really appreciate it.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
DRAW the figure.
Two right triangles share the same leg of 12 meters for the tree height. One triangle has short unknown leg where Mazaheer is, the 67 degree elevation to tree top, and longer unknown leg where Trinia is, the 53 degree angle of elevation to the tree top. The point of the tree base, point where is Mazaheer and point where is Trinia, are on the same line (collinear).

Mazaheer:
tan%2867%29=12%2FM
M%2Atan%2867%29=12
M=12%2Ftan%2867%29

Trinia:
tan%2853%29=12%2FT
T%2Atan%2853%29=12
T=12%2Ftan%2853%29

How far apart are they?
T-M
12%2Ftan%2853%29-12%2Ftan%2867%29-----this uncomputed expression is how far apart the two girls are on the ground. This itself was not what was the question. Neither is this really necessary...

How far is Trinia from the top of the tree?
This is the hypotenuse of the right triangle so, .... USE sine function.
Let r be the distance from Trinia to the tree top.
highlight%28sin%2853%29=12%2Fr%29
THAT is what you want, and solve for r.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Hey there
Trina and mazaheer are standing on the same side of a red maple tree. The angle of elevation from mazaheer to the tree top is 67 degrees and the angle of elevation from Trina to the tree top is 53°. If the tree is 12m high how far apart are the two girls? What is the distance between Trina and the top of the tree?
Can you please solve this step by step. I'm having a lot of trouble with this question. Thanks I really appreciate it. 
.

Trina is standing at the green broken line

Let Trina’s distance, from where she’s standing, to the base of the tree, be D

We then get: tan+%2853%29+=+O%2FA -------> tan+%2853%29+=+12%2FD

D * tan 53 = 12 --------- Cross-multiplying

D, or distance Trina is from the base of the tree = 12%2Ftan+%2853%29, or 9.0426 m



Mazaheer is standing at the yellow broken line

Let Mazaheer’s distance, from where she’s standing, to the base of the tree, be M

We then get: tan+%2867%29+=+O%2FA --------> tan+%2867%29+=+12%2FM

M * tan 67 = 12 --------- Cross-multiplying

M, or distance Mazaheer is from the base of the tree = 12%2Ftan+%2867%29, or 5.0937 m



Distance the two are from each other: 9.0426 – 5.0937, or highlight_green%28matrix%281%2C2%2C3.9489%2C+m%29%29



The only distance that can be calculated from Trina to the top of the tree, is from her feet to the top of the tree (green broken line, or hypotenuse line),

since her height was not given.

This becomes: sin+%2853%29+=+O%2FH -----> sin+%2853%29+=+12%2FH, with H being the distance from Trina’s feet to the top of the tree