Brenda A.

asked • 04/06/15

Sohcahtoa mountain triangle trigonometry---PLEASE HELP!!!

Sohcahtoa Mountain has an altitude of 800m. It is one of several that form the Scalenes Mountain Range. The mountain to the east of Sohcahtoa Mountain has a higher altitude. George Geometer was taking a break from skiing and was basking in the sun at the top of Sohcahtoa Mountain. He wondered how much higher the eastern mountain was. He was able to see down to the base of the mountain at an angle of 41 degrees and look up to the peak at an angle of 27 degrees. What is the altitude of Eastern Peak?

Bob A.

There is a triangle formed when George looks at the eastern mountain.

SO we need to find out the length of one of the sides.

Consider that he is sitting on SOACAHTOA 800 feet up and assume that the base of
the eastern mountain is exactly at the base of SOACAH TOA.
G below is George
EP (eastern peak)
/
/
/
G 41° down + 27° up = 68°
| \
h \
| \
SM ---- SB EB (eastern base)
(soacahtoa base)
(soacahtoa middle)

Consider the right triangle G-SB-SM
Side G-SM id the height or 800 feet
Angle SM-G-SB is 90-41 = 49°
Find side G-SB

Now to look at the eastern mpuntain
There is a triangle G-EB-EP
Angle EP-G-EB is 41+27 = 68°
Side G-SB = G-EB (remember we assumed SB and EB were the same place)
For this triangle you know 1 angle and 1 side.
As far as I can tell you are stuck at this point.

Are you sure there isn't more to the description?
The description you gave doesn't tell me all I need to know as far as I can tell.
Report

04/07/15

Bob A.

DANG Wyzant doesn't preserve spaces and formatting on a cut and paste.
Trying again ....

There is a triangle formed when George looks at the eastern mountain.
SO we need to find out the length of one of the sides.

Consider that he is sitting on SOACAHTOA 800 feet up and assume that the base of
the eastern mountain is exactly at the base of SOACAH TOA.
G below is George
                               EP (eastern peak)
                      /
            /
    /
G 41° down + 27° up = 68°
|   \
h     \
|       \
SM ---- SB EB (eastern base)
            (soacahtoa base)
(soacahtoa middle)

Consider the right triangle G-SB-SM
Side G-SM id the height or 800 feet
Angle SM-G-SB is 90-41 = 49°
Find side G-SB

Now to look at the eastern mpuntain
There is a triangle G-EB-EP
Angle EP-G-EB is 41+27 = 68°
Side G-SB = G-EB (remember we assumed SB and EB were the same place)
For this triangle you know 1 angle and 1 side.
As far as I can tell you are stuck at this point.

Are you sure there isn't more to the description?
The description you gave doesn't tell me all I need to know as far as I can tell.
Report

04/07/15

1 Expert Answer

By:

Mark M. answered • 04/07/15

Tutor
5.0 (278)

Mathematics Teacher - NCLB Highly Qualified

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Draw and label a diagram.
 
A, point of observation
B, base of mountain below A
C, base of opposite mountain opposite B
D, point on opposite mountain at height of 800 feet.
E, top of opposite mountain
 
∠BAC = 49°, ∠ACB = 41°, ∠AED = 63°
 
By the Law of Sines
 
BC / sin 49 = 800 / sin 41
BC / 0.7547 ≈ 800 / 0.6560
BC / 0.7547 ≈ 1219.51
BC ≈ 920.36
 
AD = BC
 
By Law of Sines
 
DE / sin 27 = 920.36 / sin 63
DE / 0.4540 ≈ 920.36 / 0.8910
DE / 0.4540 ≈ 103.30
DE ≈ 468.96
 
CE = CD + DE
CE = 800 + 468.96
CE = 1268.96
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