The angle of elevation of a ladder leaning against a wall is 60deg and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
Question
The angle of elevation of a ladder leaning against a wall is 60deg and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:
Solution
To solve this problem, we can use the trigonometric function of sine. The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse.
In this case, the ladder acts as the hypotenuse of the triangle, the height of the wall is the opposite side, and the distance from the wall to the ladder is the adjacent side.
The problem gives us the angle of elevation (60 degrees) and the distance from the wall to the ladder (4.6 m). We need to find the length of the ladder (the hypotenuse).
The sine of 60 degrees is √3/2. So, we can set up the equation as follows:
sin(60) = Opposite/Hypotenuse √3/2 = 4.6/Hypotenuse
Solving for the Hypotenuse gives:
Hypotenuse = 4.6 / (√3/2) Hypotenuse = 4.6 * 2/√3 Hypotenuse = 9.2/√3 Hypotenuse ≈ 5.31 m
So, the length of the ladder is approximately 5.31 meters.
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