Question

The pilot of a hot air balloon wonders how high it is. To find out, a landmark in the distance is chosen and the angle of depression to it is measured to be 54. A few minutes later, after traveling 100 feet closer, the angle of depression to the same landmark measures 61°. How high is the balloon ?

Answer 1

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Ol B 100 ft 540 DA - pc x D looft c Ambro In figure, A is the initial point of hot air balloon at h height. from point A, Angle of depression of point p on the ground y 54°. After travelling 100 ft, from A to B, angle of depression of same point ? 61. Cool LBAC = LAPC = 54° (Alternate angle LEBP = LBPC 261 (Alternate angle) PD bex. AB=CD = 10ot. Let AC be h and AC = BD = h.

52 Now, 10 In ABPD I " tan61 BD = h tan6i z and In DAPC tan 54 = AC Z. AC. mondoh to al Pc A to PD + DO tans to north no x+100 m Itan54: (x +100) = h from equation I - - DAO tanss ( h +100) = het OY 194 h. tan54° + too ansth . ist tanci tan6l

4 25 26 27 LU 0.762941 ht 137.638192=h h-0.762941 h = 137.638192 0.237059 h = 137.638192 h = 137.638192 0.237059 42 580.607226 The 580.61 feet - s Hence the height of hot air batoon 580.61 feets. Au