Posted by **Ghanny** on Monday, April 12, 2010 at 10:20am.

Two observers who are 5 km apart simultaneously sight a small airplane flying between them. One observer measures a 51.0-degree inclination angle, while the other observer measures a 40.5-degree inclination angle. At what altitude is the

airplane flying?

- math help pls -
**Reiny**, Monday, April 12, 2010 at 11:12am
Draw a triangle ABC , A and B the position of the observers and C the position of the plane.

Drop an altitude from C to AB, call it CD.

Label angle A as 51 and angle B as 40.5 degrees

Label AD as x, then DB = 5-x

In triangle ACD, cot51 = x/h

x = hcot51

In triangle DBC cot 40.5 = (5-x)/h

5-x = hcot40.5 or

x = 5 - hcot40.5

then hcot51 = 5-hcot40.5

hcot51 + hcot40.5 = 5

h = 5/(cot51 + cot40.5)

= .....

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