Select the correct answerA ladder lean against the wall makes angle of elevation of 60° with the ground. If the length of the ladder is 19m, Find the distance of the foot of the ladder from the wall?Options9m18m9.5m6
Question
Select the correct answerA ladder lean against the wall makes angle of elevation of 60° with the ground. If the length of the ladder is 19m, Find the distance of the foot of the ladder from the wall?Options9m18m9.5m6
Solution
The problem involves a right triangle where the ladder acts as the hypotenuse. The angle of elevation is given as 60°. We are asked to find the distance of the foot of the ladder from the wall, which is the base of the triangle.
We can use the trigonometric function cosine (cos) to solve this problem. The cosine of an angle in a right triangle is equal to the adjacent side (base) divided by the hypotenuse.
So, cos(60°) = base / hypotenuse
We know that cos(60°) = 0.5 and the hypotenuse (the ladder) is 19m.
So, 0.5 = base / 19m
Solving for base, we get base = 0.5 * 19m = 9.5m
So, the distance of the foot of the ladder from the wall is 9.5m. Therefore, the correct answer is 9.5m.
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