Question

A ladder 5 m long, leaning against a vertical wall makes an angle of 65˚ with the ground.

a. how high on the wall does the ladder reach? round to the nearest tenth of a meter.
b. how far is the foot of the ladder from the wall? round to the nearest tenth of a meter.

Answer 1

The height the ladder reaches on the wall and the distance from the wall are found using the sine and cosine of the 65° angle with trigonometry, using the 5 m length of the ladder.

Step-by-step explanation:

To determine how high a ladder reaches up a wall, one can use trigonometric functions based on the given angle and the length of the ladder. Since the ladder makes a 65° angle with the ground and the length of the ladder is 5 meters, you can use the cosine and sine functions to find the respective distances.

To find the height on the wall (opposite side), we use the sine function:
Height = ladder_length * sin(angle) = 5 * sin(65°).

To find the distance from the wall (adjacent side), we use the cosine function:
Distance = ladder_length * cos(angle) = 5 * cos(65°).