Question 1

Which of the following best describes the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Accepted Answer

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

Question 2

Given a right triangle with legs of length 5 and 12, what is the length of the hypotenuse?

Accepted Answer

$$\sqrt{5^2$ + 12^2$} = 13$$

Question 3

If a point $$P$$ has coordinates $$(x, y)$$ and is at a distance $$r$$ from the origin, which equation correctly represents $$r$$?

Accepted Answer

$$r = \sqrt{x^2$ + y^2$}$$

Question 4

Which of the following sets is a Pythagorean triple?

Accepted Answer

$$3, 4, 5$$

Question 5

A ladder is leaning against a wall, forming a right triangle with the ground. If the base of the ladder is 6 ft from the wall and the ladder is 10 ft long, how high up the wall does the ladder reach?

Accepted Answer

$$\sqrt{10^2$ - 6^2$} = 8 ft$$

Question 6

Which of the following statements is true about the hypotenuse in a right triangle?

Accepted Answer

It is always the side opposite the right angle.

Question 7

If $$P is a $$point on the terminal side of an angle in standard position with coordinates $$(7, 24)$$, what is the distance from $$P to $$the origin?

Accepted Answer

$$\sqrt{7^2$ + 24^2$} = 25$$

Question 8

Which of the following is NOT a property of a Pythagorean triple?

Accepted Answer

All three numbers are always even.

Question 9

A right triangle has legs of length $$x$$ and $$y. If$$ $$x = 9$$ and the hypotenuse is $$15$$, what is $$y$$?

Accepted Answer

$$y = \sqrt{15^2$ - 9^2$} = 12$$

Question 10

Which of the following best explains why the Pythagorean Theorem is important in trigonometry?

Accepted Answer

It relates the sides of a right triangle, which is fundamental for defining trigonometric functions.

Question 11

If a point $$P is at$$ $$(x, y)$$ and $$r = 10$$, which of the following could be the coordinates of $$P$$?

Accepted Answer

$$(6, 8)$$

Question 12

A surveyor needs to find the distance across a river. She places markers at points $$A$$ and $$B on $$one side of the river, 12 meters apart. She then measures the distance from $$A to a $$point $$C$$ directly across the river as 13 meters. What is the width of the river?

Accepted Answer

$$\sqrt{13^2$ - 12^2$} = 5$$ meters

Question 13

Which of the following is a correct application of the Pythagorean Theorem in the coordinate plane?

Accepted Answer

The distance from $$(0,0) to$$ $$(x, y) is$$ $$\sqrt{x^2$ + y^2$}.$$

Question 14

If the legs of a right triangle are both 1 unit long, what is the length of the hypotenuse?

Accepted Answer

$$\sqrt{1^2$ + 1^2$} = \sqrt{2}$$

Question 15

Which of the following is a real-world application of the Pythagorean Theorem?

Accepted Answer

Finding the straight-line distance between two points on a map.

Trigonometric Functions and the Pythagorean Theorem

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