# Video: CBSE Class X • Pack 5 • 2014 • Question 4

CBSE Class X • Pack 5 • 2014 • Question 4

02:31

### Video Transcript

A ladder resting against a vertical wall makes an angle of 60 degrees with the ground. If the foot of the ladder is two metres from the base of the wall, what is the length of the ladder? Give your answer as an exact number of metres.

Let’s start by drawing a diagram of what’s happening here. So we have a ladder leaning up against a wall. We’re told that the wall is vertical, and this means that the angle between the wall and the ground is 90 degrees. So we can mark a right angle on our diagram. Also, we’re told that the ladder makes an angle of 60 degrees with the ground, so we can mark this on our diagram as well. The final piece of information that the question gives us is that the foot of the ladder is two metres from the base of the wall. And so we can add this final piece of information onto our diagram.

Now when we look at our diagram, we can see that we have a right-angled triangle, where we know one of the side lengths and one of the angles other than the right angle. Now the question asked us to find the length of the ladder, and that is this length here, which is also the hypotenuse of our right-angled triangle.

In order to find the length 𝑙, we can use SOHCAHTOA. Let’s start by labelling the adjacent side, the opposite side, and the hypotenuse on our triangle. So the hypotenuse is this side which is opposite the right angle. The opposite is the side which is opposite the known angle. And the adjacent is the shorter side next to the known angle.

So we know the length of the adjacent, and we’re looking to find the length of the hypotenuse. So therefore we need to use CAH since this involves both the adjacent and the hypotenuse. We have that the hypotenuse is equal to the adjacent over cos 𝜃. And our adjacent here is two metres, 𝜃 is our angle of 60 degrees, and our hypotenuse is the length 𝑙. So we obtain that 𝑙 is equal to two over cos 60.

Next, we can use the fact that cos of 60 is simply equal to one-half. And we obtain that 𝑙 is equal to two divided by one-half. And when we’re dividing by a fraction, this is the same as multiplying by the reciprocal of that fraction. And so we obtain that this is equal to two multiplied by two over one. But two over one is simply just two, and so we get the solution that the length of our ladder, 𝑙, is equal to four metres.