2016 Question Paper Solution | Question 3

This is an easy 1-mark question from the chapter Applications of Trigonometry. Concept tested: applying trigonometric ratios to compute the length of one side of a right triangle when an angle and another side of a right triangle are given.

Question 3: A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.

Video Explanation

Explanatory Answer | Q3 2016 Board Paper

AC is the ladder and AB is the wall. C is the foot of the ladder which is 2.5 m away from the wall.
In right ΔABC, AC is the hypotenuse

In the given triangle, the distance between the foot of the ladder and the wall (BC) is the adjacent side to ∠ACB
The length of the ladder, AC is the hypotenuse of the right triangle.

The trigonometric ratio of the adjacent side (BC) and hypotenuse (AC) is Cosθ
cos 60° = \\frac{BC}{AC})
cos 60° = \\frac{1}{2}) and BC = 2.5 m
So, \\frac{1}{2}) = \\frac{2.5}{AC})
or AC = 5 m
Length of the ladder = 5 m.