Question 1

Given a triangle with sides $$a = 7$$, $$b = 9$$, and angle $$C = 35^	ext{o}$$, which formula would you use to find the length of side $$c$$?

Accepted Answer

The Law of Cosines: $$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$ \cos C$$

Question 2

Using the Law of Cosines, calculate the length of side $$c$$ for a triangle with $$a = 7$$, $$b = 9$$, and $$C = 35^	ext{o}. $$Which of the following is closest to the correct answer?

Accepted Answer

$$c \approx 5.7$$

Question 3

Which of the following is the correct Law of Sines equation for a triangle with sides $$a$$, $$b$$, $$c$$ and opposite angles $$A$$, $$B$$, $$C$$?

Accepted Answer

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

Question 4

A surveyor measures two sides of a triangular plot of land as $$a = 120 m $$and $$b = 150 m$$, with the angle between them $$C = 60^	ext{o}. $$What is the area of the plot?

Accepted Answer

$$A = 7794.23 m$^2$$

Question 5

If $$a = 8$$, $$b = 15$$, and $$C = 45^	ext{o}$$, what is the value of $$c$$ using the Law of Cosines?

Accepted Answer

$$c = \sqrt{8^2$ + 15^2$ - 2 \cdot 8 \cdot 15 \cdot \cos 45^	ext{o}}$$

Question 6

Which scenario best describes when to use the Law of Sines instead of the Law of Cosines?

Accepted Answer

When you know two angles and one side.

Question 7

A triangle has $$A = 40^	ext{o}$$, $$B = 60^	ext{o}$$, and $$a = 10. $$What is the length of side $$b$$?

Accepted Answer

$$b = 10 \cdot \frac{\sin 60^	ext{o}}{\sin 40^	ext{o}}$$

Question 8

A pilot needs to calculate the distance between two cities using triangulation. If the angle at the airport is $$50^	ext{o}$$ and the distances to the cities are $$a = 200 km $$and $$b = 250 km$$, what formula should be used to find the distance between the cities?

Accepted Answer

Law of Cosines

Question 9

Which of the following is NOT a valid application of the Law of Sines?

Accepted Answer

Finding the area of a triangle when all three sides are known.

Question 10

A triangle has sides $$a = 5$$, $$b = 7$$, and $$c = 10. $$Which formula would you use to find angle $$C$$?

Accepted Answer

Law of Cosines

Question 11

A construction engineer needs to find the height of a triangular support beam. If the base is $$12 m$$, the side is $$15 m$$, and the angle between them is $$30^	ext{o}$$, what is the height?

Accepted Answer

$$h = 15 \cdot \sin 30^	ext{o}$$

Question 12

Which of the following is the correct rearrangement of the Law of Cosines to solve for angle $$C$$?

Accepted Answer

$$\cos C = \frac{a^2$ + b^2$ - c^2$}{2ab}$$

Question 13

A triangle has $$a = 6$$, $$b = 8$$, and $$C = 90^	ext{o}. $$What is the length of side $$c$$?

Accepted Answer

$$c = \sqrt{6^2$ + 8^2$}$$

Question 14

Which of the following is a real-world application of the Law of Sines?

Accepted Answer

Calculating the height of a mountain using angles and distances measured from two points.

The Law of Sines in Trigonometry

Guida di studio - Domande di pratica

Study guide - Flashcard