Q52. A ladder is leaning on a buildin... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q52. (page 659)

A ladder is leaning on a building. The base of the ladder is 10 feetfrom the building, and the ladder reaches up 15 feeton the building. How long is the ladder?

Short Answer

Expert verified

The ladder is $5 \sqrt{13}$ feet long

Step by step solution

Step 1. Given.

The base of the ladder $= 10 feet$

The ladder reaches up to a height of 15 feet

Step 2. Draw the rough sketch for the given problem.

The rough sketch for the given problem is:

$A C$ is the building and $C E$ is the ground.

$B C$ is the height up to which ladder can reach on the building.

$C D$ is the distance of the base of the ladder from the building.

$B D$ is the ladder.

Step 3. Determine the length of the ladder.

In the triangle $B C D$ , $鈭� B C D$ is a right angle. Therefore, the triangle $B C D$ is right-angled.

According to the Pythagorean theorem, it can be noticed that:

${(B D)}^{2} = {(B C)}^{2} + {(C D)}^{2}$

Therefore,

${(B D)}^{2} = {(B C)}^{2} + {(C D)}^{2} {(B D)}^{2} = {(15)}^{2} + {(10)}^{2} {(B D)}^{2} = 225 + 100 {(B D)}^{2} = 325 B D = \sqrt{325} B D = \sqrt{25 脳 13} B D = \sqrt{5^{2} 脳 13} B D = 5 \sqrt{13}$

Therefore, the ladder is $5 \sqrt{13}$ feet long.

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91影视

A ladder is leaning on a building. The base of the ladder is 10 feetfrom the building, and the ladder reaches up 15 feeton the building. How long is the ladder?

Short Answer

Step by step solution

Step 1. Given.

Step 2. Draw the rough sketch for the given problem.

Step 3. Determine the length of the ladder.

One App. One Place for Learning.

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