A 19-f ladder is leaning against a wall and the wall is perpendicular to the ground. The base of the ladder is 8 ft from the wall. How high above the ground is the top of
the ladder?
The ladder reaches
(Simplify your answer. Type an exact answer, using radicals as needed.)

Question

UpStudy AI · Accepted Answer

To find the height of the top of the ladder above the ground, we can use the Pythagorean theorem.

Given:
- Length of the ladder = 19 ft
- Distance from the base of the ladder to the wall = 8 ft

Let's denote the height of the top of the ladder above the ground as $$ h $$.

Using the Pythagorean theorem:
$$ h^2 + 8^2 = 19^2 $$

Now, we can solve for $$ h $$ to find the height of the top of the ladder above the ground.
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$h^{2}+8^{2}=19^{2}$$
- step1: Evaluate the power:
  $$h^{2}+64=19^{2}$$
- step2: Add or subtract both sides:
  $$h^{2}=297$$
- step3: Simplify the expression:
  $$h=\pm \sqrt{297}$$
- step4: Simplify the expression:
  $$h=\pm 3\sqrt{33}$$
- step5: Separate into possible cases:
  $$\begin{align}&h=3\sqrt{33}\&h=-3\sqrt{33}\end{align}$$
- step6: Rewrite:
  $$h_{1}=-3\sqrt{33},h_{2}=3\sqrt{33}$$
The height of the top of the ladder above the ground is either $$ -3\sqrt{33} $$ ft or $$ 3\sqrt{33} $$ ft. Since height cannot be negative, the height of the top of the ladder above the ground is $$ 3\sqrt{33} $$ ft.
The height of the top of the ladder above the ground is $$ 3\sqrt{33} $$ ft.

A 19-f ladder is leaning against a wall and the wall is perpendicular to the ground. The base of the ladder is 8 ft from the wall. How high above the ground is the top of
the ladder?
The ladder reaches
(Simplify your answer. Type an exact answer, using radicals as needed.)

Upstudy AI Solution

Answer

Solution

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A 19-f ladder is leaning against a wall and the wall is perpendicular to the ground. The base of the ladder is 8 ft from the wall. How high above the ground is the top of the ladder? The ladder reaches (Simplify your answer. Type an exact answer, using radicals as needed.)

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Geometry Questions

A 19-f ladder is leaning against a wall and the wall is perpendicular to the ground. The base of the ladder is 8 ft from the wall. How high above the ground is the top of
the ladder?
The ladder reaches
(Simplify your answer. Type an exact answer, using radicals as needed.)