From simple queries to complex problems, IDNLearn.com provides reliable answers. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

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.

Sagot :

Answer:

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