Final answer:
By using the sine function given the angle of 76° and the distance from the wall to the base of the ladder, the vertical distance of a ladder from the ground to the top is approximately 0.4 m, which corresponds to answer option (a).
Step-by-step explanation:
To determine the vertical distance of the ladder from the ground to the top, we can use trigonometry, specifically the sine function which deals with the opposite side of an angle in a right-angled triangle. The ladder forms the hypotenuse, the vertical wall forms one side, and the ground forms the base of the triangle. Given an angle of 76° and the distance from the wall to the base of the ladder (1.8 meters), we can use the sine function:
sin(76°) = Opposite / Hypotenuse
Let the vertical distance be the opposite side (O), and the hypotenuse (H) is the length of the ladder we want to find. Rearranging the formula:
O = H × sin(76°)
Since the base of the triangle is given, and we want to find the opposite side, we can write:
O = 1.8 m / tan(76°)
Now solve for O:
O = 1.8 m / tan(76°) ≈ 1.8 m / 4.0108 ≈ 0.4489 m
Rounding to the nearest tenth gives 0.4 m as the vertical distance from the ground to the top of the ladder.
The correct answer is (a) 0.4 m.