Question 1

In a 45-45-90 triangle, if one leg has length $$7$$, what is the length of the hypotenuse?

Accepted Answer

$$7 \sqrt{2}$$

Question 2

Which of the following is the correct ratio of the sides in a 30-60-90 triangle?

Accepted Answer

$$1 : \sqrt{3} : 2$$

Question 3

A ladder leans against a wall forming a $$45^{\circ}$$ angle with the ground. If the distance from the ground to the top of the ladder is $$10$$ feet, how long is the ladder?

Accepted Answer

$$10\sqrt{2}$$ feet

Question 4

If the hypotenuse of a 30-60-90 triangle is $$12$$, what is the length of the side opposite the $$30^{\circ}$$ angle?

Accepted Answer

$$6$$

Question 5

Which trigonometric value is correct for a $$45^{\circ}$$ angle in a 45-45-90 triangle?

Accepted Answer

$$\sin 45$$^{\circ}$$ = \dfrac{\sqrt{2}}{2}$$

Question 6

A triangle has sides $$x$$, $$x$$, and $$x\sqrt{2}. $$What are the measures of its angles?

Accepted Answer

$$45^{\circ}$$, $$45^{\circ}$$, $$90^{\circ}$$

Question 7

If the shorter leg of a 30-60-90 triangle is $$8$$, what is the length of the longer leg?

Accepted Answer

$$8\sqrt{3}$$

Question 8

Which of the following is the value of $$	an 30$$^{\circ}$$?

Accepted Answer

$$\dfrac{1}{\sqrt{3}}$$

Question 9

A right triangle has angles $$30^{\circ}$$, $$60^{\circ}$$, and $$90^{\circ}. If $$the side opposite the $$60^{\circ}$$ angle is $$9$$, what is the hypotenuse?

Accepted Answer

$$6\sqrt{3}$$

Question 10

Without using a calculator, for which angle $$A in$$ $$[0$$^{\circ}$$, 90$$^{\circ}$$]$$ does $$\cos A = \dfrac{\sqrt{2}}{2}$$?

Accepted Answer

$$45^{\circ}$$ only

Question 11

If the hypotenuse of a 45-45-90 triangle is $$10$$, what is the length of each leg?

Accepted Answer

$$5\sqrt{2}$$

Question 12

Which trigonometric value is correct for a $$60^{\circ}$$ angle in a 30-60-90 triangle?

Accepted Answer

$$\sin 60$$^{\circ}$$ = \dfrac{\sqrt{3}}{2}$$

Question 13

A triangle has sides $$5$$, $$5\sqrt{3}$$, and $$10. $$What are the measures of its angles?

Accepted Answer

$$30^{\circ}$$, $$60^{\circ}$$, $$90^{\circ}$$

Question 14

If the longer leg of a 30-60-90 triangle is $$15$$, what is the length of the shorter leg?

Accepted Answer

$$5\sqrt{3}$$

Question 15

Which of the following is the value of $$	an 45$$^{\circ}$$?

Accepted Answer

$$1$$

Question 16

A triangle has a hypotenuse of $$20$$ and one angle of $$45^{\circ}. $$What is the length of each leg?

Accepted Answer

$$10\sqrt{2}$$

Question 17

If $$\cos A = \dfrac{1}{2}$$ for $$A in$$ $$[0$$^{\circ}$$, 90$$^{\circ}$$]$$, what is $$A$$?

Accepted Answer

$$60^{\circ}$$

Question 18

A ramp rises at a $$30^{\circ}$$ angle. If the ramp is $$10$$ meters long, how high does it rise?

Accepted Answer

$$5$$ meters

Question 19

Which of the following is the value of $$\cos 60$$^{\circ}$$?

Accepted Answer

$$\dfrac{1}{2}$$

Question 20

If the side opposite the $$30^{\circ}$$ angle in a 30-60-90 triangle is $$x$$, what is the length of the hypotenuse?

Accepted Answer

$$2x$$

Special Right Triangles: 45-45-90 and 30-60-90 Triangles

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