Question

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is???
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Answer 1

CONCEPT :

Firstly draw the appropriate figure as per conditions given in question. Whenever we have a right angle in a triangle we can use the trigonometry concept to find the unknown length. Here in this case, the angle between bases of the line joining bases of the ladder and wall and the height of the wall is 90°, so we can easily apply the trigonometric concept. While using trigonometric tools, choose that ration which includes the length of one given side and unknown side as we know the value of sin 60° in this question.

GIVEN :

• A ladder 15 m long just reaches the top of a vertical wall.

• If the ladder makes an angle of 60°

TO FIND :

• What is the height of the wall

SOLUTION :

➦ Let AC be the ladder of length 15 m, AB be the wall. Now ∠ B = 90° and ∠ C = 60°.

➦ In triangle ABC,

➦ Sin30∘ = AB / AC

Now,

➦ Given, AC = 15 m

➦ 1 / 2 = AB / 15

➦ AB / = 15 / 2

➦ AB = 15 × 0.5 = 15 / 2

Thus, the height of wall is 7.5 m

So, the correct answer is “7.5 m”.