Q: Does the set of numbers $$7$$, $$16$$, and $$18$$ form a Pythagorean triple?

No, because $$7^2$$ + $$16^2$$ \neq $$18^2$$

Question 1

Given a triangle with side lengths $$a = 9$$, $$b = 12$$, and $$c = x$$, use the Pythagorean Theorem to find the value of $$x.$$

Accepted Answer

$$x = \sqrt{9^2$ + 12^2$} = \sqrt{81 + 144} = \sqrt{225} = 15$$

Question 2

Does the set of numbers $$6$$, $$8$$, and $$10$$ form a Pythagorean triple?

Accepted Answer

Yes, because $$6^2$$ + $$8^2$$ = $$10^2$$

Question 3

Does the set of numbers $$7$$, $$16$$, and $$18$$ form a Pythagorean triple?

Accepted Answer

No, because $$7^2$$ + $$16^2$$ 
eq $$18^2$$

Question 4

A window washer uses an 18-ft ladder to reach a window 16 feet above the ground. How far from the building should the base of the ladder be placed? Round your answer to the nearest tenth.

Accepted Answer

$$\sqrt{18^2$ - 16^2$} = \sqrt{324 - 256} = \sqrt{68} \approx 8.2 ft$$

Question 5

A square has a diagonal of $$12 cm. $$What is the perimeter of the square? Express your answer in simplest radical form.

Accepted Answer

$$24 cm$$

Question 6

Given triangle side lengths $$3$$, $$4$$, and $$6$$, classify the triangle as acute, right, or obtuse.

Accepted Answer

Obtuse, because $$6^2$$ \u003e $$3^2$$ + $$4^2$$

Question 7

Given triangle side lengths $$9$$, $$11$$, and $$16$$, classify the triangle as acute, right, or obtuse.

Accepted Answer

Obtuse, because $$16^2$$ \u003e $$9^2$$ + $$11^2$$

Question 8

Given triangle side lengths $$4$$, $$6$$, and $$7$$, classify the triangle as acute, right, or obtuse.

Accepted Answer

Acute, because $$7^2$$ \u003c $$4^2$$ + $$6^2$$

Question 9

If a triangle has side lengths $$a$$, $$b$$, and $$c ($$with $$c as $$the largest), which condition must be true for the triangle to be a right triangle?

Accepted Answer

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

Question 10

A triangle has side lengths $$a = 5$$, $$b = 12$$, and $$c = 13. Is $$this triangle a right triangle?

Accepted Answer

Yes, because $$13^2$$ = $$5^2$$ + $$12^2$$

Question 11

A triangle has side lengths $$a = 8$$, $$b = 15$$, and $$c = 17. Is $$this triangle a right triangle?

Accepted Answer

Yes, because $$17^2$$ = $$8^2$$ + $$15^2$$

Question 12

A triangle has side lengths $$a = 7$$, $$b = 24$$, and $$c = 25. Is $$this triangle a right triangle?

Accepted Answer

Yes, because $$25^2$$ = $$7^2$$ + $$24^2$$

Question 13

Given two integers $$33$$ and $$55$$, which value of $$j$$ would make $$33$$, $$55$$, and $$j$$ the side lengths of an acute triangle?

Accepted Answer

$$j \u003c \sqrt{33^2$ + 55^2$}$$

Question 14

Given two integers $$33$$ and $$55$$, which value of $$k$$ would make $$33$$, $$55$$, and $$k$$ the side lengths of an obtuse triangle?

Accepted Answer

$$k \u003e \sqrt{33^2$ + 55^2$}$$

Question 15

A construction worker needs to place a ladder to reach a window 10 feet above the ground. If the ladder is 13 feet long, how far from the wall should the base be placed?

Accepted Answer

$$\sqrt{13^2$ - 10^2$} = \sqrt{169 - 100} = \sqrt{69} \approx 8.3 ft$$

Question 16

A square has a side length $$s. $$What is the length of its diagonal?

Accepted Answer

$$s\sqrt{2}$$

Question 17

A triangle has side lengths $$a = 10$$, $$b = 24$$, and $$c = 26. Is $$this triangle a right triangle?

Accepted Answer

Yes, because $$26^2$$ = $$10^2$$ + $$24^2$$

Question 18

A triangle has side lengths $$a = 8$$, $$b = 15$$, and $$c = 20. $$Classify the triangle as acute, right, or obtuse.

Accepted Answer

Obtuse, because $$20^2$$ \u003e $$8^2$$ + $$15^2$$

Guided Practice: The Pythagorean Theorem and Triangle Classification

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