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Umnica [9.8K]
3 years ago
7

A 10-foot ladder touches the side of a building at a point 8 feet above the ground. At what height would a 22-foot ladder touch

the building if it makes the same angle with the ground as the shorter ladder? Round to the nearest tenth if necessary.
Mathematics
1 answer:
WARRIOR [948]3 years ago
6 0
<h2>Answer:</h2>

8.75 feet

<h2>Step by step:</h2>

Given that a 12 foot ladder leans against a building seven feet above the ground.

By using trigonometry ratio, the angle between the ladder and the ground will be

SinØ = opposite/ hypothenus

SinØ = 7 / 12

SinØ = 0.58333

Ø = Sin^-1(0.58333)

Ø = 35.69 degree

At what height would an 15 foot ladder touch the building if both ladders form the same angle with the ground?

Using the same trigonometric ratios

SinØ = opposite/hypothenus

Sin 35.69 = opposite/ 15

Cross multiply

Opposite = 15 × sin 35.69

Opposite = 8.75 feet

Therefore, the ladder will touch the building if both ladders form the same angle with the ground at height 8.75 feet.

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