# A 12 foot-ladder is resting against a wall. The base of the ladder is 2.5 feet from the base of the wall.How high up the wall will the ladder reach?

Jun 1, 2018

#### Answer:

$\approx 11.74 f t .$

#### Explanation:

${a}^{2} + {b}^{2} = {c}^{2}$

c = 12

b = 2.5

${a}^{2} + {2.5}^{2} = {12}^{2}$

${a}^{2} + 6.25 = 144$

${a}^{2} = 137.75$

$a = \pm \sqrt{137.75}$

$a \approx \pm 11.74$

We can ignore the negative value because a the length has to be positive:

$\approx 11.74 f t .$