# TRIG Question!

#### swish

Here is the problem.

1. Ted is flying a kite with a string that makes an angle of 40 degrees with the horizontal. If the kite is 750 feet high, how long is the string?

and
2. Rita is estimating the height of a tree. From a point due east of the tree, the angle of elevation to the top is 27degrees. She walks 200 feet toward the tree and the angle of elevation increases to 39 degrees.
How tall is tree?

how far from the base of the tree was rita standing when she first observed the tree?

How do I know when to use Cosine and Tangent? I don't get it - and how do I know when to divide/multiply them? Please help.

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#### greg1313

Forum Staff
1. Ted is flying a kite with a string that makes an angle of 40 degrees with the horizontal. If the kite is 750 feet high, how long is the string?

Let x be the length of the string. Using the sine ratio, sin(40) = 750/x, x = 750/sin(40) â‰ˆ 1166.7929.

2. Rita is estimating the height of a tree. From a point due east of the tree, the angle of elevation to the top is 27degrees. She walks 200 feet toward the tree and the angle of elevation increases to 39 degrees.
How tall is tree?

Here's one way to do it:

Let T be the height of the tree. Let x be the distance from Rita to the tree after she walks 200 feet towards the tree.

tan(39) = T/x, x = T/tan(39) (*)

tan(27) = T/(200 + x) (**)

Substitute x from (*) into (**):

tan(27) = T/(200 + T/tan(39))

(200 + T/tan(39))tan(27) = T

200tan(27) + tan(27)T/tan(39) = T

200tan(27) = T - tan(27)T/tan(39)

200tan(27) = T(1 - tan(27)/tan(39))

T = 200tan(27)/(1 - tan(27)/tan(39)) â‰ˆ 274.8335.

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#### skipjack

Forum Staff
2. Make a diagram if you find it awkward to imagine one.