Height of tree Homework problem

AI Thread Summary
To determine the height of a tree from a distance of 76 meters at an angle of 32 degrees, trigonometric functions can be applied. The calculations using cosine and sine yield values of 64 and 40, respectively, but the height is more accurately found using the tangent function. By applying the formula for the opposite side, the height is calculated as 76 times the tangent of 32 degrees, resulting in approximately 47.5 meters. The initial estimate of 75 meters seems incorrect based on these calculations. Therefore, the height of the tree is approximately 47 meters.
bengaltiger14
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Suppose there is a tree of unknown height. I am standing 76 meters away from the tree and the top of the tree is 32 degrees from where I am standing. Could I find the height of the tree by this:

76 cos(32) =64
76 sin(32) =40

Magnitude = SQRT 64^2 + 40^2
Height of Tree equals 75 meters??
 
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I may be wrong, but:

Opposite = adjacent * Tan angle
= 76 * Tan 32
= 47.5

Is that one of your answers? If not, forget I replied. :D
 
I think that is the right way. I think 47 meters is the correct answer.
 
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