# is this correct? 10 points for best answer..?

14. Two friends observe a hot-air balloon directly in line between them. Sara determines the angle of elevation to be 65 and Suki measures the angle of elevation to be 55. The girls mark their spots and then measure the distance between the markers. They determine this distance to be 285 m. Determine the height of the balloon to the nearest metre from a point directly below.

The point on the ground directly below the balloon is P.

AP = x

BP = 285 - x

In triangle ACP, tan 65 = CP/x => x = CP/tan 65

x = 0.466 CP

In triangle BCP, tan 55 = CP/(285 - x)

=> 285 - x = CP/tan 55 = 0.7 CP

285 - 0.466 CP = 0.7 CP

(0.7 + 0.466) CP = 285

CP = 285/(0.7 + 0.466) = 244.38 m.

The height of the balloon to the nearest metre is 244.38 m.

### 2 Answers

- TwiggyLv 71 decade agoBest Answer
I`m assuming that C is the position of the balloon. You seem to have got the angles of elevation incorrect. If C is the position of the ballon, then in triangle ACP, tan 55 = CP/x, and in triangle BCP, tan 65 = CP/(285 - x).

Hope this helps, Twiggy.

- mechamLv 43 years ago
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