A ladder leans against a brick wall. The ladder itself is 20 feet long. The ladder reaches a height of 15 feet on the wall. How do you find the angle of elevation the ladder makes with the ground?

1 Answer
Mar 9, 2018

The angle of elevation is #48.59^o#

Explanation:

Using the function #sin#, we can find the desired angle. It is helpful, first of all, to draw a picture. H is the ladder, O is the building, and A is the ground . As you can see, it looks like a triangle:

https://www.allaboutcircuits.com/textbook/reference/chpt-5/right-triangle-trigonometry/
We know some of the lengths in this diagram.
H = 20
O = 15

We are trying to find #/_ x#, because that is the "angle of elevation the ladder makes with the ground". There are 3 functions used to find angles in a right triangle by dividing different sides of the triangle. They are: #tan = A/O, sin = (O)/H, cos = A/H#

Which of these do we use? Well, which of these functions do we know the values of? The only one with both #O# and #H# is #sin#, so that is the function we will use.

#sin /_x = (O)/H#

#sin /_x = 15/20#

#sin /_x = 0.75#

Now, using your calculator, hit #2nd# and then #sin#. This will find the angle that make this decimal. It should say: #48.59#, so we know that:

#/_x =48.59^o#