Precalculus with Trigonometry right triangle word problems?

Question

ill just ask the first one and see if i can figure the rest out if you can help me! plz be super detailed how you do this i was absent when she went over this

The tallest freestanding structure in the world is 553-m tall CN tower in toronto, ontario. Suppose that at a certain time of day it casts a shadow 1100m long on the ground. What is the angle of elevation of the sun at the time of day?

THANKS SOOOOOOOOOOOOOO MUCH IF U HELP!

Answer 1

This system can be modeled as a right triangle.  

We will use the tangent function to find angle of elevation.

From the definition of the tangent function:

tan(Θ) = a/b  , where a is the length of the side opposite Θ and b is the length of the side adjacent to Θ.

In this problem Θ is the angle between the ground and the top of the CN tower with the Sun in the line of sight.  Also a = 553 m and b = 1100 m.

For further clarification there is a decent illustration of this at http://asd-www.larc.nasa.gov/SCOOL/gifs/...

In the figure the ruler represents the CN tower.  The angle at C is Θ and b (length of the shadow) is the distance from B to C.

We solve for Θ using the inverse of tangent:

tan(a/b)^-1 = Θ

tan(553/1100)^-1 = 26.7°  This is our angle of elevation.