Question

A ladder that is 6 metres long is placed against a wall. It

makes an angle of 34° with the wall.

a. Find how high up the wall it reaches (2dp)

b. Find the distance the base of the ladder is away from the

wall(2dp)

Answer 1

Using trigonometry, the height the ladder reaches up the wall is calculated to be 3.35 meters, and the distance from the base of the ladder to the wall is found to be 4.99 meters.

Step-by-step explanation:

The question involves a ladder resting against a wall and requires the use of trigonometry to solve for two distances: the height the ladder reaches up the wall, and the distance from the base of the ladder to the wall. The ladder forms a right-angled triangle with the wall and the ground. We're given the hypotenuse (6m) and an angle (34°).

To find the height up the wall (opposite side), we use the sine function: Height = Hypotenuse × Sine(Angle). To find the base (adjacent side), we use the cosine function: Base = Hypotenuse × Cosine(Angle).

So,

1. Height up the wall = 6 × sin(34°) = 6 × 0.559 = 3.35 meters (2dp)
2. Base distance from the wall = 6 × cos(34°) = 6 × 0.832 = 4.99 meters (2dp)

Answer 2

To solve for the height the ladder reaches up the wall and the distance from the base of the ladder to the wall, we apply trigonometric functions. The height is approximately 3.38 m and the distance is about 4.99 m.

Step-by-step explanation:

The student is asking about the height a ladder reaches up a wall and the distance from the base of the ladder to the wall when the ladder makes a 34° angle with the wall. To solve this problem, we use trigonometric ratios from a right-angled triangle formed by the ladder, wall, and ground. Specifically, we can use the sine and cosine functions from trigonometry.

To find the height up the wall (opposite side of the angle), we use the sine function:

• sin(34°) = Opposite/Hypotenuse
• sin(34°) = Opposite/6 m
• Opposite = 6 m × sin(34°)
• Opposite ≈ 3.38 m (after calculating 2dp)

To find the distance from the base of the ladder to the wall (adjacent side of the angle), we use the cosine function:

• cos(34°) = Adjacent/Hypotenuse
• cos(34°) = Adjacent/6 m
• Adjacent = 6 m × cos(34°)
• Adjacent ≈ 4.99 m (after calculating 2dp)