### Video Transcript

A ladder leaning against a wall
makes an angle of 60 degrees with the horizontal. If the foot of the ladder is 2.5
meters away from the wall, find the length of the ladder.

First, let’s sketch what we
know. We have a wall and a ladder. The foot of the ladder is 2.5
meters away from the wall. The ladder makes a 60-degree angle
with the horizontal. The horizontal is here. And this is our 60-degree
angle. We need to find the length of the
ladder, this measure. We need to know that there is a
right angle between the horizontal and the wall.

In this problem, we have an
adjacent side length and a hypotenuse. Since we know that this creates a
right angle, we can set up a ratio of the cosine of our angle. Cosine of 60 degrees equals the
adjacent side length, 2.5, over the hypotenuse side length, 𝑙, that we’re
missing. We recognize that cosine of 60
degrees is one-half. So we substitute one-half for
cosine of 60 degrees. And now, we have one-half equals
2.5 over 𝑙.

There’s a few ways to think about
this. One way is to think that the ratio
one over two is one in the numerator multiplied by two to get the denominator. To keep these ratios the same, that
would mean, on the right-hand side, we would need to multiply the numerator by two
to get the denominator. 2.5 times two equals five. And the ladder is five meters
tall.

However, if you didn’t recognize
this relationship, you could multiply both sides of the equation by two. On the left, you would get one. And on the right, you would now
have five over 𝑙. And then, we would multiply both
sides of the equation by 𝑙, to find again 𝑙 equals five. The length of the ladder is five
meters.