Q: If $$\sin \theta = 0.6$$ and $$\theta is in $$the second quadrant, what is $$\theta$$?

$$\theta = 180^\circ - \arcsin(0.6)$$

Q: A flagpole casts a shadow 123 ft long. If the angle of elevation to the top of the pole is $$26^\circ 40'$$, what is the height of the flagpole?

$$h = 123 \tan 26^\circ 40' \approx 61.9 ft$$

Q: If $$\cos(\theta) = -\dfrac{1}{2}$$ and $$\theta is $$between $$90^\circ$$ and $$270^\circ$$, what are the possible values for $$\theta$$?

$$\theta = 120^\circ or$$ $$\theta = 240^\circ$$

Question 1

In the right triangle shown in the first image, if $$A is $$the angle at the origin, which of the following correctly expresses $$\sin A in $$terms of $$x$$, $$y$$, and $$r$$?

Accepted Answer

$$\sin A = \dfrac{y}{r}$$

Question 2

Given the triangle in the second image, what is $$\cos 30^\circ$$?

Accepted Answer

$$\cos 30^\circ = \dfrac{\sqrt{3}}{2}$$

Question 3

Which of the following is the reference angle for $$210^\circ as $$shown in the fourth image?

Accepted Answer

$$30^\circ$$

Question 4

A car weighing 2500 lb is traveling uphill on a $$6^\circ$$ grade (see the seventh image). What is the grade resistance force $$F to $$the nearest 10 lb? (Use $$F = W \sin 	heta.)$$

Accepted Answer

$$F \approx 260 lb$$

Question 5

In the triangle with sides $$a = 29.43 cm $$and $$c = 53.58 cm ($$see the tenth image), what is $$\sin A$$?

Accepted Answer

$$\sin A = \dfrac{29.43}{53.58}$$

Question 6

If $$\cos 	heta = 0.5$$ and $$	heta is an $$acute angle, what is $$	heta$$?

Accepted Answer

$$	heta = 30^\circ$$

Question 7

Which of the following is a cofunction identity?

Accepted Answer

$$\sin(90^\circ - A) = \cos A$$

Question 8

A surveyor uses a subtense bar of length $$b = 2.0000 cm $$and measures an angle $$	heta = 1.5^\circ ($$see the fifteenth image). What is the distance $$d$$ between the points? (Use $$d = \dfrac{b}{2 	an(	heta/2)}.)$$

Accepted Answer

$$d \approx 76.4 cm$$

Question 9

If $$	an 	heta = 1$$ and $$	heta is in $$the second quadrant, what is $$	heta$$?

Accepted Answer

$$	heta = 135^\circ$$

Question 10

A ship leaves port and sails on a bearing of N $$47^\circ E $$for 3.5 hr at 22 knots, then turns and sails on a bearing of S $$43^\circ E $$for 4.0 hr at the same speed. What is the total distance traveled?

Accepted Answer

$$165$$ nautical miles

Question 11

Which of the following best describes the angle of depression?

Accepted Answer

The angle formed by a downward line of sight and a horizontal line

Question 12

If $$\sin 	heta = 0.6$$ and $$	heta is in $$the second quadrant, what is $$	heta$$?

Accepted Answer

$$	heta = 180^\circ - \arcsin(0.6)$$

Question 13

Which of the following is the correct value for $$	an 60^\circ$$?

Accepted Answer

$$	an 60^\circ = \sqrt{3}$$

Question 14

A flagpole casts a shadow 123 ft long. If the angle of elevation to the top of the pole is $$26^\circ 40'$$, what is the height of the flagpole?

Accepted Answer

$$h = 123 	an 26^\circ 40' \approx 61.9 ft$$

Question 15

Which of the following is true about the signs of trigonometric functions in the four quadrants?

Accepted Answer

Sine is positive in Quadrants I and II

Question 16

If $$\sin(	heta) = \cos(30^\circ)$$ and $$	heta is $$acute, what is $$	heta$$?

Accepted Answer

$$	heta = 60^\circ$$

Question 17

A right triangle has legs of length 24 and 7 (see the fifth image). What is the sine of the angle at $$A$$?

Accepted Answer

$$\sin A = \dfrac{7}{25}$$

Question 18

Which calculator mode should be used when evaluating $$\sin(45^\circ)$$?

Accepted Answer

Degree mode

Question 19

If $$\cos(	heta) = -\dfrac{1}{2}$$ and $$	heta is $$between $$90^\circ$$ and $$270^\circ$$, what are the possible values for $$	heta$$?

Accepted Answer

$$	heta = 120^\circ or$$ $$	heta = 240^\circ$$

Chapter 2: Acute Angles and Right Triangles – Trigonometric Functions and Applications

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