SOLUTION: A surveyor standing next to a hut on one side of a river sights a boulder on the other side and determines the angle from the hut to the boulder is 70o. She then walks 100 meters

Algebra ->  Trigonometry-basics -> SOLUTION: A surveyor standing next to a hut on one side of a river sights a boulder on the other side and determines the angle from the hut to the boulder is 70o. She then walks 100 meters       Log On


   

Question 1148857: A surveyor standing next to a hut on one side of a river sights a boulder on the other side and determines the angle from the hut to the boulder is 70o. She then walks 100 meters parallel to the river until she arrives at a tree. The angle to the boulder from the tree is 32o. How far from the hut is the boulder?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A surveyor standing next to a hut on one side of a river sights a boulder on the other side and determines the angle from the hut to the boulder is 70o.
She then walks 100 meters parallel to the river until she arrives at a tree.
The angle to the boulder from the tree is 32o.
How far from the hut is the boulder?
:
Draw this out as a triangle, we can find the 3 angles:
32 degrees
180 - 70 = 110 degrees
180 - 32 - 110 = 38 degrees
:
Using the law of sines, find the dist from the hut to the bolder (s)
s%2Fsin%2832%29 = 100%2Fsin%2838%29
cross multiply
sin(38)*s = sin(32)*100
:
s = %28%28sin%2832%29%2A100%29%29%2Fsin%2838%29
s = 86.1 meters