The base of a 13 foot ladder is 5 feet away from the wall. how far up the wall does the ladder reach? a)8 feet b)10 feet c)12 feet d)18

You are solving for the height. Use the formula:

c² - b² = a²      in which c = hypotenuse

(13)² - (5)² = a²

Simplify

169 - 25 = a²

144 = a²

Isolate the a. Root both sides

√144 = √a²

a = √144

a = √(12 x 12)

a = 12

C) 12 feet is your answer

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We can Notice from the Diagram that the Ladder with Wall Forms a Right Angled Triangle.

We know that In A Right Angles Triangle :

(Hypotenuse)² = (First Leg)² + (Second Leg)²

Here the Hypotenuse is the Length of Ladder and One of the Leg is Length away from the Wall

Substituting the Respective Values, We get :

⇒ 5² + (Second Leg)² = 13²

⇒ 25 + (Second Leg)² = 169

⇒ (Second Leg)² = 169 - 25

⇒ (Second Leg)² = 144

⇒ Second Leg = 12 Feet

⇒ The Ladder reaches a Height of 12 Feet

Option C is the Answer

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