Math algebra 2 plz help me

Question

What is the height of a tree if the end of its shadow is 70 feet from the trunk when the sun is 

 above the horizon. Round to the nearest foot. 

Answer 1

As other tutors have noted in the comments, you left out the angle of elevation of the sun and a numerical answer cannot be given without it. However, the procedure for the solution can be given.

Let x be the missing angle of elevation of the sun and h be the height of the tree. It's important in problems like this to draw a diagram and to find a triangle that will help you solve the problem:

1. Draw a line from the base of the tree to the end of its shadow. This line is 70 feet long and forms one leg of the triangle
2. Draw another line from the base of the tree to its top. This line is the height of the tree, h. The line forms a right angle with the side you drew in step 1
3. Finally draw a line from the top of the tree to the tip of its shadow on the ground. This line is the hypotenuse of the triangle, Angle x - the elevation angle of the sun, is the angle between this line and the ground

You now have a right triangle and can state the following relation:

tan(x) = h/70

70 tan(x) = h

So plug in the value of x (angle of the sun above the ground) given in your problem and use your calculator to find h. The units are feet.