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

(84-8)/x = tan 60°

Now just solve for x

To find the distance from the burning building where the base of the fire truck ladder should be placed, we can use trigonometry. Here's how you can calculate it step by step:

1. Draw a right triangle to represent the situation. The vertical side of the triangle corresponds to the height of the burning building, which is 84 ft. The horizontal side represents the distance from the base of the ladder to the building. The hypotenuse is the length of the ladder.

|
|
| 84 ft
|
|___________
/|
/ |
/ |
/ |
Ladder / |
/ |
/ |
/ |
/________|

2. Since we know the height of the building and the angle formed by the ladder with the ground, we can find the length of the ladder using trigonometry. The ladder is the hypotenuse, and the height of the building is the opposite side, so we can use the sine ratio:

sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = 84 ft/hypotenuse

Rearranging the equation, we get:

hypotenuse = 84 ft / sin(60 degrees)

Using a calculator, we find that sin(60 degrees) ≈ 0.866. So,

hypotenuse ≈ 84 ft / 0.866

3. Calculate the length of the hypotenuse (ladder):

hypotenuse ≈ 97 ft (rounded to the nearest foot)

4. Now, we need to find the distance from the base of the ladder to the building. In the right triangle, the horizontal side represents this distance, and the height of the truck (8 ft) is the opposite side. Since we already know the hypotenuse (ladder length) is approximately 97 ft, we can use the sine ratio again:

sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = 8 ft/horizontal side

Rearranging the equation, we get:

horizontal side = 8 ft / sin(60 degrees)

Using a calculator, we find that sin(60 degrees) ≈ 0.866. So,

horizontal side ≈ 8 ft / 0.866

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

horizontal side ≈ 9.24 ft (rounded to the nearest foot)

Therefore, the base of the fire truck ladder should be placed approximately 9.24 feet away from the burning building to reach the top of the building at an angle of 60 degrees with the ground.