SOLUTION: 'A hiker sights the top of a 2228 m high mountain at an angle of elevation of 12�.After walking towards the mountain he sights it at an angle of elevation of 22�. How many kilometr

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Question 907197: 'A hiker sights the top of a 2228 m high mountain at an angle of elevation of 12�.After walking towards the mountain he sights it at an angle of elevation of 22�. How many kilometres did the hiker walk?'
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Answer by ankor@dixie-net.com(22740) (Show Source):
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'A hiker sights the top of a 2228 m high mountain at an angle of elevation of 12�.
After walking towards the mountain he sights it at an angle of elevation of 22�.
How many kilometres did the hiker walk?'
:
We can use a right triangle formed by the hiker position to a point directly below the top of the mountain
Use the tangent of 12 degrees, where 2228 is the side opposite, find the distance (d) to the point below the top of the mountain (side adjacent)
tan(12) =
.2125565
d =
d = 10482 meters
:
Do the same from the point that has an angle of 22 degrees
tan(22) =
d =
d = 5514.5 meters
Therefore the hiker walked
10482 - 5514.5 = 4967.5 meters which is 4.9675 km