Autumn B.

asked • 03/12/17

Setting up the trig equation. Using sine or cosine.

Tami and Dustin are on opposite sides of the washington monument, which is 555 feet. Tami's angle of elevation to the top of the monument is 38 degrees. Dustin's angle of elevation is 64 degrees. To the nearest foot, how far apart are tami and dustin?

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Kenneth S. answered • 03/12/17

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Draw and label a stick figure of this situation...two right triangles sharing the same vertical leg 555' in height.
 
Call the distance from base of monument to Tami a, and the distance from base to Dustin b.
 
tan 38o = 555/a;  tan 64o = 555/b.  Now you can solve for  a and b  (be sure calculator is in degree mode).
 
Answer: a+b.
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Autumn B.

Would I treat both as if they were 2 separate right triangles? Also would you use law of cosine then?
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03/12/17

Kenneth S.

Two separate right triangles; two separate statements; two separate calculations (for b & a). Those triangles are fused together, sharing the same hypotenuse (the Wash. Monument).  No Law of Cosines needed.
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03/12/17

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