A 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?Options18m9.5m69m
Question
A 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?Options18m9.5m69m
Solution
To solve this problem, we can use trigonometric functions. In this case, we will use the cosine function.
The cosine of an angle in a right triangle is equal to the adjacent side (which is the distance from the wall to the ladder's foot we are looking for) divided by the hypotenuse (which is the length of the ladder).
So, we have:
cos(60°) = adjacent side / hypotenuse
We know that the hypotenuse is 19m, so we can substitute this into the equation:
cos(60°) = adjacent side / 19m
We know that cos(60°) = 0.5, so:
0.5 = adjacent side / 19m
To solve for the adjacent side, we multiply both sides by 19m:
0.5 * 19m = adjacent side
So, the adjacent side, which is the distance from the wall to the foot of the ladder, is 9.5m.
Therefore, the correct answer is 9.5m.
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