Question

The corner of a room where two walls meet the floor should be a right triangle. Jeff makes a mark along each wall. One mark is 15 inches from the corner. The other is 8 inches from the corner. How can Jeff use the Pythagorean Theorem to see if the walls form a right​ angle?

Answer 1

USED PYHTOGOREAN THEOREM

Explanation:

GIVEN: The corner of a room where two walls meet the floor should be a right triangle. Jeff makes a mark along each wall. One mark is
`15` inches from the corner. The other is
`8` inches from the corner.

TO FIND: How can Jeff use the Pythagorean Theorem to see if the walls form a right​ angle.

SOLUTION:

Consider the figure attached.

Let first mark that is
`15` inches from wall be
`\text{A}`

Let the second mark that is
`8` inches from wall be
`\text{B}`

Now to check whether the corner is right angle we will use Pythagorean theorem.

Pythagorean theorem states that the square of side that is hypotenuse is equal to the sum of squares of other two sides in a right angle triangle.

applying it

`\text{AB}^2=\text{AO}^2+\text{BO}^2`

`\text{AO}=15\text{ and }\text{BO}=8`

`\text{AB}^2=15^2+8^2`

`\text{AB}^2=289`

`\text{AB}=17`

using Pythagorean theorem direct distance between both marks is
`17\text{ inches}`

Now, Jeff can measure the direct distance between both marks, if it is
`17\text{ inches}`, the Pythagorean theorem holds true for it and corner forms a right angle.