math
posted by donovan .
Richard is standing between two buildings in a town house development.The building on the left is 9 m away and the angle of elevation to its security spotlight A is 68 degrees. The building on the right is 6m away and the angle of elevation to its security spotlight B is 73 degrees which spotlight is farther away from ricchard and by how much ?

Richard is standing between two buildings in a town house development.The building on the left is 9 m away and the angle of elevation to its security spotlight A is 68 degrees. The building on the right is 6m away and the angle of elevation to its security spotlight B is 73 degrees which spotlight is farther away from ricchard and by how much ?

We draw 2 rt triangles:
X1 = 9 m. = Hor side.
Y1 = Ht. of light(L1) = Ver. side.
Ae = 68 Deg. = Angle of elevation.
Z1 = Hyp. = X1/cosAe = 9 / cos68=24 m.=
Dist. from Rich. to L1.
X2 = 6 m. = Hor. side.
Y2 = Ht. of L2 = Ver side.
Be = 73 Deg. = Angle of elevation.
Z2 = Hyp. = X2/cosBe = 6 / cos73=20.5 m
Z1  Z2 = 24  20.5 = 3.5 m.
Therefore, the spotlight on the left is 3.5 m farther away.
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