### 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.