From a point 87 feet from the base of a tree, the angle of elevation is 53 degrees. The distance from the tree is how many feet?

Question

I need to know the distance from the standing point to the top of the tree.

Answer 1

Hi Corey.

 

To solve this, you need to draw a right triangle.  

 

The vertical leg represents the tree.

The horizontal leg represents the ground.

The hypotenuse (diagonal) is the distance from the standing point to the top of the three.

 

The 53 degrees is the angle between the ground (horizontal leg) and the hypotenuse.

The horizontal leg is 87 feet.

 

Circle the vertex with the 53 degrees written in it, and look IN TOWARDS THE CENTER OF THE TRIANGLE.  The 87 feet should be the adjacent side and the unknown (I called it x) should be on the hypotenuse.

 

The Trig function that uses the adjacent side and the hypotenuse is the COSINE.

 

So set up the equation

 

cos(53) = 87/x       then solve for x.  Be sure your calculator is in DEGREES mode, not radians.

 

Multiply both sides by x.

 

x cos(53) = 87

 

Divide both sides by "cos(53)"

 

x = 87/cos(53)

 

And type that into your calculator.  I get x = 144.6 feet