A ladder on a fire truck has its base 8 feet above the ground. The maximum length of the ladder is 100 feet. If the greatest acute angle the ladder can make with the truck is 70°, what is the highest it can reach?

101.97 feet above the ground

Step-by-step explanation:

To obtain the highest reach of the ladder, the ladder would have to be used to its maximum length (100 feet) and the greatest acute angle.

The ladder, the truck and the wall (this is assumed to be what the ladder leans on, in this case) form a right angled triangle, with the ladder as the hypotenuse, the truck as the adjacent and the wall as the opposite side. A description of this is shown in the attached image.

Using the formula, Sin (given angle) = , we have that

Opposite = Sin (given angle) × Hypotenuse

Opposite = Sin (70 degrees) × 100 feet

Opposite = 0.9397 × 100 feet = 93.97 feet

The total height of the ladder from the ground will be (93.97 + 8) feet = 101.97 feet

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step-by-step explanation:

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