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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