# trig

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Sandra wants to find the height of a moutain. From her first location on the ground, she finds the angle of elevation to the top of the mountain to be 35 degrees 15 minutes. After moving 1000 meters closer to the moutain on level ground, she finds the elevation to be 50 degrees and 25 minutes . Find the height of the moutain to the nearest foot

• trig -

make a sketch labeling the height of the mountain as PQ, with P as the top of the mountain.
Label the 2 points of observation as A and B, with B the closer point,
In triang ABP,
angle A = 35°15'
angle ABP = 180 - 50°25' = 129°35'
then angle APB = 15°10'
and AB = 1000 m

by the sine law:
BP/sin35°15' = 1000/sin15°10'
BP = 2205.9788..

now in the right-angled triangle BPQ
PQ/PB = sin50°25'
PQ = Height of mountain = 1700.145 m
or appr 1700 m

Did you want the answer in feet?
Why did you have metric units ?
I will let you do the conversion, if needed.

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