6sin^2theta = 7- 5costheta

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6sin^2(x) = 7 - 5cos(x)

6(1 - cos^2(x)) = 7 - 5cos(x)

6 - 6cos^2(x) = 7 - 5cos(x)

6cos^2(x) + 5cos(x) -1 = 0

(6cos(x) - 1)(cos(x) + 1) = 0

cos(x) = 1/6

x = arccos(1/6)

x = 1.40334825 + 2k*pi, 4.87983706 + 2k*pi

cos(x) = -1

x = pi + 2k*pi

you estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 .the total height of the building is another 123 meters above the 86th floor.

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