The tower of a tower crane casts a shadow (on level ground) of 32 m when the sun is 55° above the horizon. What is the height of the tower?assuming that the ground slopes upward at 1:5 from the base of the crane to the end of the shadow, as shown.

Explanation:

Well, which is it, level ground or sloping upward at a ratio of 1 m rise for every 5 m of run?

I will ASSUME you mean the shadow is 32 m long as measured along the 1:5 slope and the sun is 55° above the horizon.

The ground slope to horizon is

arctan (1/5) = 11.31°

The "top" end of the shadow is above the tower base by

32sin11.31 = 6.2757 m

The "top" end of the shadow is a horizontal distance from the tower base of

32cos11.31 = 31.3786 m

The tower height above the "top" of the shadow is

h = 31.3786tan55 = 44.8132 m

so the tower height is

44.8132 + 6.2757 = 51.0889 = 51 m

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