Q: Given a right triangle where one angle is $$30^\\circ$$ and the hypotenuse is 10 units, what is the length of the side opposite the $$30^\\circ$$ angle?

$$10 \\times \\sin(30^\\circ)$$

Q: Which equation represents the Pythagorean identity?

$$\\sin^2$(\\theta) + \\cos^2$(\\theta) = 1$$

Q: Which of the following is the correct formula for the tangent of an angle in a right triangle?

$$\\tan(\\theta) = \\frac{\\text{opposite}}{\\text{adjacent}}$$

Q: A ramp rises 2 meters vertically and is 5 meters long. What is the angle of elevation of the ramp?

$$\\sin$$^{-1}$$(\\frac{2}{5})$$

Q: A surveyor measures the angle of elevation to the top of a building as $$40^\\circ$$ from a point 50 meters away. What is the height of the building?

$$50 \\times \\tan(40^\\circ)$$

Q: Which of the following is the correct formula for the law of sines?

$$\\frac{a}{\\sin(A)} = \\frac{b}{\\sin(B)} = \\frac{c}{\\sin(C)}$$

Q: A ship sails 100 km east, then turns $$30^\\circ$$ north of east and sails another 50 km. What is the total displacement from the starting point?

$$\\sqrt{100^2$ + 50^2$ + 2 \\times 100 \\times 50 \\times \\cos(30^\\circ)}$$

Q: Which of the following is the correct formula for the law of cosines?

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$\\cos(C)$$

Q: A Ferris wheel has a radius of 20 meters. What is the height above the ground of a seat at an angle of $$90^\\circ$$ from the lowest point?

$$20 \\times \\sin(90^\\circ)$$

Question 1

Which of the following is the correct definition of the sine function for a right triangle?

Accepted Answer

The ratio of the opposite side to the hypotenuse.

Question 2

Given a right triangle where one angle is $$30^\circ$$ and the hypotenuse is 10 units, what is the length of the side opposite the $$30^\circ$$ angle?

Accepted Answer

$$10 \times \sin(30^\circ)$$

Question 3

If $$\sin(\theta) = 0.6$$, what is $$\theta in $$degrees?

Accepted Answer

$$\theta = 53.13^\circ$$

Question 4

Which equation represents the Pythagorean identity?

Accepted Answer

$$\sin^2$(\theta) + \cos^2$(\theta) = 1$$

Question 5

A ladder leans against a wall making a $$60^\circ$$ angle with the ground. If the ladder is 8 meters long, how high up the wall does it reach?

Accepted Answer

$$8 \times \sin(60^\circ)$$

Question 6

Which of the following is the correct formula for the tangent of an angle in a right triangle?

Accepted Answer

$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$

Question 7

If $$\cos(\theta) = 0.5$$, what is $$\theta in $$degrees?

Accepted Answer

$$\theta = 60^\circ$$

Question 8

A ramp rises 2 meters vertically and is 5 meters long. What is the angle of elevation of the ramp?

Accepted Answer

$$\sin$$^{-1}$$(\frac{2}{5})$$

Question 9

Which of the following is the correct expression for the area $$A of a $$triangle given two sides $$a$$ and $$b$$ and the included angle $$C$$?

Accepted Answer

$$A = \frac{1}{2}ab\sin(C)$$

Question 10

If $$\tan(\theta) = 1$$, what is $$\theta in $$degrees?

Accepted Answer

$$\theta = 45^\circ$$

Question 11

A surveyor measures the angle of elevation to the top of a building as $$40^\circ$$ from a point 50 meters away. What is the height of the building?

Accepted Answer

$$50 \times \tan(40^\circ)$$

Question 12

Which of the following is the correct formula for the law of sines?

Accepted Answer

$$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$$

Question 13

If $$\sin(\theta) = \frac{3}{5}$$ and $$\theta is in $$the first quadrant, what is $$\cos(\theta)$$?

Accepted Answer

$$\frac{4}{5}$$

Question 14

A ship sails 100 km east, then turns $$30^\circ$$ north of east and sails another 50 km. What is the total displacement from the starting point?

Accepted Answer

$$\sqrt{100^2$ + 50^2$ + 2 \times 100 \times 50 \times \cos(30^\circ)}$$

Question 15

Which of the following is the correct formula for the law of cosines?

Accepted Answer

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$\cos(C)$$

Question 16

A Ferris wheel has a radius of 20 meters. What is the height above the ground of a seat at an angle of $$90^\circ$$ from the lowest point?

Accepted Answer

$$20 \times \sin(90^\circ)$$

Question 17

If $$\tan(\theta) = 2$$ and $$\theta is in $$the first quadrant, what is $$\sin(\theta)$$?

Accepted Answer

$$\frac{2}{\sqrt{5}}$$

Question 18

A building casts a shadow of 15 meters when the sun's angle of elevation is $$45^\circ. $$What is the height of the building?

Accepted Answer

$$15 \times \tan(45^\circ)$$

Question 19

Which of the following is the correct expression for the double angle formula for sine?

Accepted Answer

$$\sin(2\theta) = 2\sin(\theta)\cos(\theta)$$

Graphing Quadratic Functions and Equations

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