how far from an 84 foot burning building should the base of the fire truck ladder be placed to reach the top of the building at an angle of 60 degrees with the ground. the ladder is mounted to the truck 8 ft off the ground

The ladder is the hyp. of a rt. triangle

X = ?
Y1 = 8 Ft.
Y2 = 84-8 = 76 Ft.
A = 60o

Tan 60 = Y2/X = 76/X
X = 76/Tan60 = 43.88 Ft. = Dist. from
bldg.

To determine the distance from the burning building to place the base of the fire truck ladder, we can use trigonometry.

Let's assume the distance from the base of the fire truck ladder to the building is x feet.

We can form a right triangle where the height of the building (opposite side) is 84 feet, the height of the ladder above the ground (opposite side) is 8 feet, and the distance from the ladder base to the building (adjacent side) is x feet.

Using the trigonometric ratio for tangent (tan) in a right triangle:

tan(60 degrees) = opposite / adjacent
tan(60 degrees) = (84 feet + 8 feet) / x
√3 = 92 / x

Cross-multiplying:
x * √3 = 92

Dividing both sides by √3:
x = 92 / √3

Approximately, x ≈ 53.169 feet.

Therefore, the base of the fire truck ladder should be placed approximately 53.169 feet from the burning building.

To find the distance from the burning building where the base of the fire truck ladder should be placed, we can use trigonometry. Let's break down the problem step by step:

1. First, draw a diagram to visualize the situation. Draw a right triangle where the vertical side represents the height of the building (84 feet) and the horizontal side represents the distance from the base of the ladder to the building.

|
| /
| /
| /
---------

Building (84 ft)

2. Since we know the angle between the ground and the ladder (60 degrees) and the height of the building (opposite side), we can use the trigonometric function tangent (tan) to find the distance we need.

tan(angle) = opposite / adjacent

tan(60 degrees) = 84 feet / adjacent

3. Solve for the adjacent side (distance from the base of the ladder to the building):

adjacent = 84 feet / tan(60 degrees)

4. Evaluate the tangent of 60 degrees:

tan(60 degrees) ≈ 1.7321

5. Calculate the distance from the base of the ladder to the building:

adjacent = 84 feet / 1.7321 ≈ 48.44 feet

Therefore, the base of the fire truck ladder should be placed approximately 48.44 feet away from the burning building to reach the top at a 60-degree angle with the ground.