A 22 m long ladder rests against a wall with its foot on the ground. It makes…
2020
A 22 m long ladder rests against a wall with its foot on the ground. It makes an angle of 30° with the wall. What is the distance (in m) from the foot of the ladder to the wall?
- A.
11√3 / 2
- B.
11
- C.
11√2
- D.
11√3
Show answer & explanation
Correct answer: B
CONCEPT: In a right triangle, when an angle is measured between the hypotenuse and a vertical side, the horizontal base is the side opposite that angle. Therefore, base = hypotenuse × sin(angle).
APPLICATION:
The ladder is the hypotenuse, so h = 22 m.
The angle between the ladder and the wall is 30°, so the ground distance d = 22 × sin 30°.
Since sin 30° = 1/2, d = 22 × 1/2 = 11 m.
CROSS-CHECK: The height up the wall would be 22 × cos 30° = 11√3 m, which appears as another option, so it is not the ground distance. Hence the required distance is 11 m.