Question

A ​15 foot ladder is leaning against a​ building, with the base of the ladder 4 feet from the building. How high up on the building will the top of the ladder​ reach?
The ladder will reach
android:
nothing ft high up on the building.
​(Round to the nearest​ tenth.)
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Answer 1

Answer: The height of the building = 14.5 feet.

Step-by-step explanation:

Given: Length of ladder = 15 feet

Distance of base of ladder from building = 4 feet

Since building is standing vertical on ground making right angle.

So with ladder a right triangle is formed , where base = 4 feet , Hypotenuse = 15 feet [Hypotenuse is side opposite to right angle]

According to the Pythagoras theorem ,

Hypotenuse² = Perpendicular² + Base²

⇒ (15)² =  Perpendicular² +  (4)²

⇒ 225 = Perpendicular² +16

⇒ Perpendicular² = 225 -16

⇒ Perpendicular² = 209

⇒  Perpendicular = √209 = 14.4568322948 ≈ 14.5 feet

Hence, the height of the building = 14.5 feet.