Video: CBSE Class X • Pack 3 • 2016 • Question 3

CBSE Class X • Pack 3 • 2016 • Question 3

02:20

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.

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