Question

A 14.5 m fire truck ladder is leaning against a wall. find the distance d the ladder goes up the wall if the ladder makes an angle of 40 degrees and 44 minutes with the horizontal

Answer 1

The distance the ladder goes up the wall is approximately 9.54 meters.

Step-by-step explanation:

To find the distance the ladder goes up the wall, we can use trigonometry. The ladder forms a right triangle with the wall and the ground. The angle between the ladder and the horizontal is given as 40 degrees and 44 minutes, which can be converted to decimal form as 40.7333 degrees. We can use the sine function to find the height of the triangle:

d = L * sin(angle)

where L is the length of the ladder and angle is the angle between the ladder and the horizontal. Substituting in the given values, we have:

d = 14.5m * sin(40.7333°)

Solving for d gives us:

d ≈ 9.54m