A ladder is leaning against a brick building as shown in the figure. What
is the length of the ladder?
x ft
20 ft
15 ft

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/

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

2

n

d

and then

sin

. This will find the angle that make this decimal. It should say:

48.59

, so we know that:

∠

x

=

48.59

25 ft

Step-by-step explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

15^2 + 20 ^2 = x^2

225+400= x^2

625 = x^2

Take the square root of each side

sqrt(625) = sqrt(x^2)

25 = x