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Chapter 10: Problem 54

In your own words, state the Pythagorean Theorem.

Short Answer

Expert verified
The Pythagorean theorem, in simple terms, states that in a right-angled triangle, the square of the longest side equals the sum of the squares of the other two sides.

Step by step solution

01

Understand the terms

In geometry, a right triangle is a triangle in which one angle is a right angle (90 degrees). The sides of a right triangle are called the base, perpendicular, and hypotenuse. The hypotenuse is the side opposite the right angle, and it is the longest side.
02

Pythagoras' Theorem Original Statement

Pythagoras' theorem originally states that in any right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This can be written as \(a^{2} + b^{2} = c^{2}\), where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
03

Rewording Pythagoras' Theorem

Given this understanding, in simpler words, the theorem can be stated as: 'For any triangle that has a right angle (90 degrees), the square of the longest side equals the sum of the squares of the other two sides.'

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Most popular questions from this chapter

In the 1939 movie The Wizard of \(\mathrm{Oz}_{z}\), upon being presented with a Th.D. (Doctor of Thinkology), the Scarecrow proudly exclaims, "The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side." Did the Scarecrow get the Pythagorean Theorem right? In particular, describe four errors in the Scarecrow's statement.

Describe each type of angle: acute, right, obtuse, and straight.

A rectangular kitchen floor measures 12 feet by 15 feet. A stove on the floor has a rectangular base measuring 3 feet by 4 feet, and a refrigerator covers a rectangular area of the floor measuring 4 feet by 5 feet. How many square feet of tile will be needed to cover the kitchen floor not counting the area used by the stove and the refrigerator?

A wheelchair ramp must be constructed so that the slope is not more than 1 inch of rise for every 1 foot of run, so I used the tangent ratio to determine the maximum angle that the ramp can make with the ground.

A wheelchair ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 23 -foot ramp, to the nearest tenth of a degree, if its final height is 6 feet.
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