Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.