Geometry Unit 4: Right Triangles and Trigonometry

The Pythagorean theorem and its converse, special right triangles, sine, cosine and tangent, and inverse trig. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Pythagorean theoremNo calculator

A right triangle has legs 9 and 12. How long is the hypotenuse?

1. $\sqrt{63}$
2. $15$
3. $21$
4. $225$

Question 2

Pythagorean theoremNo calculator

The hypotenuse of a right triangle is 13 and one leg is 5. How long is the other leg?

1. $18$
2. $12$
3. $\sqrt{194}$
4. $8$

Question 3

Pythagorean theoremCalculator

A 20-foot ladder leans against a wall with its foot 6 feet from the wall. How high up the wall does it reach, to the nearest tenth of a foot?

1. $19.1$
2. $20.9$
3. $14.0$
4. $19.0$

Question 4

Special right trianglesNo calculator

A $45^\circ$-$45^\circ$-$90^\circ$ triangle has legs of length 7. How long is the hypotenuse?

1. $14$
2. $7\sqrt{3}$
3. $7\sqrt{2}$
4. $\frac{7\sqrt{2}}{2}$

Question 5

Special right trianglesNo calculator

In a $30^\circ$-$60^\circ$-$90^\circ$ triangle, the shorter leg is 5. How long is the longer leg?

1. $5\sqrt{3}$
2. $\frac{5\sqrt{3}}{3}$
3. $10$
4. $5\sqrt{2}$

Question 6

Trigonometric ratiosNo calculator

In right triangle $ABC$, the right angle is at $C$, $AC=8$, $BC=15$ and $AB=17$. What is $\sin A$?

1. $\frac{15}{17}$
2. $\frac{8}{15}$
3. $\frac{15}{8}$
4. $\frac{8}{17}$

Question 7

Finding sidesCalculator

In a right triangle, one acute angle is $35^\circ$ and the hypotenuse is 20. How long is the side opposite the $35^\circ$ angle, to the nearest tenth?

1. $14.0$
2. $16.4$
3. $11.4$
4. $11.5$

Question 8

Angles of elevationCalculator

From a point on level ground 50 feet from the base of a building, the angle of elevation to the top is $62^\circ$. How tall is the building, to the nearest foot?

1. $27$
2. $107$
3. $94$
4. $44$

Question 9

Inverse trigonometryCalculator

A kite string 10 meters long is pulled straight, and the kite is 7 meters higher than the hand holding it. What angle does the string make with the horizontal, to the nearest degree?

1. $44$
2. $35$
3. $45$
4. $46$

Question 10

CofunctionsNo calculator

If $\sin x^\circ=0.6$, what is $\cos(90-x)^\circ$?

1. $0.6$
2. $0.4$
3. $1.67$
4. $0.8$

Question 11

Converse of the Pythagorean theoremNo calculator

Which set of side lengths makes a right triangle?

1. 7, 24, 26
2. 8, 15, 17
3. 5, 11, 12
4. 6, 9, 12

Question 12

Inverse trigonometryCalculator

A ramp rises 2 feet over a horizontal distance of 24 feet. What angle does it make with the ground, to the nearest tenth of a degree?

1. $85.2$
2. $0.1$
3. $4.7$
4. $4.8$