Quiz about Law of Cosines Formula

Question 1

Given the Law of Cosines formula ,solve for .NOTE THAT THERE ARE 2 CORRECT CHOICES. One choice results from isolating on the right side of the equation, while the other choice results from isolating on the left side of the equation. To get on the left side of the equation, we need to add to both sides of the equation.

Accepted Answer

$$A=\cos^{-1}\left(\frac{\left(b^2+c^2-a^2\right)}{2bc}\right)$$

Accepted Answer

$$A=\cos^{-1}\left(\frac{\left(a^2-b^2-c^2\right)}{-2bc}\right)$$

Answer

$$A=\cos^{-1}\left(\frac{\left(a^2-b^2-c^2\right)}{2bc}\right)$$

Answer

$$A=\cos\left(\frac{\left(a^2-b^2-c^2\right)}{-2bc}\right)$$

Question 2

Which Law would you use?

Accepted Answer

Law of Cosines

Answer

Law of Sines

Answer

Law of the Jungle

Answer

Law of Gravity

Question 3

Find XZ

Accepted Answer

34.7 meters

Answer

16.004 meters

Answer

544.165 meters

Answer

1204.165 meters

Question 4

Which Law would you use?

Accepted Answer

Law of Cosines

Answer

Law of Sines

Answer

Law of the Jungle

Answer

Law of Gravity

Question 5

What is the distance across the river? The two sides are 4.15 miles and 5.33 miles. The included angle measure is 37 degrees.

Accepted Answer

3.2 miles

Answer

2.9 miles

Answer

3.6 miles

Answer

3.9 miles

Question 6

A pilot flying over Norfolk airport is told he will have to redirect and land in either Richmond or Raleigh. Due to air traffic, he is then told he must land in Raleigh. Find the distance he will travel.

Accepted Answer

151 miles

Answer

143 miles

Answer

127 miles

Answer

160 miles

Question 7

Imagine you're an architect designing a triangular garden. Two sides of the garden are planned to be $$a = 5$$ meters and $$b = 12$$ meters long, respectively, with the angle between them set at $$ heta = 120^\circ$$ . Calculate the length of the third side of the garden, denoted as $$c$$ .

Accepted Answer

13 meters

Answer

14 meters

Answer

15 meters

Answer

16 meters

Question 8

If you know the lengths of three sides to a triangle, what formula can you use to find an angle measure?

Accepted Answer

Law of Cosine

Answer

Law of Sine

Answer

Law of Tangent

Answer

Law of Sign

Question 9

Which of the following formulas shows the Law of Cosines?

Accepted Answer

c² = a² + b² - 2abcosC

Answer

c² = a² + b² - 4ac + cosA

Answer

c² = a² - b² - 2abcosC

Answer

(cos A)/a = (cos B)/b

Question 10

Which Law would you use?

Accepted Answer

Law of Cosines

Answer

Law of Sines

Answer

Law of the Jungle

Answer

Law of Gravity

Question 11

Find the exact area of the triangle

Accepted Answer

13.9 in2

Answer

13.8 in2

Answer

14.0 in2

Answer

27.9 in2

Question 12

What is the length of side x?

Accepted Answer

105 cm

Answer

130 cm

Answer

112 cm

Answer

150 cm

Law of Cosines Formula

20 questions

Given the Law of Cosines formula \(a^2=b^2+c^2-2bc\cos A\), solve for \(a\).

Find the length of Side BC.

Find AB

Which Law would you use?

Find XZ

Which Law would you use?

What is the distance across the river? The two sides are 4.15 miles and 5.33 miles. The included angle measure is 37 degrees.

A pilot flying over Norfolk airport is told he will have to redirect and land in either Richmond or Raleigh. Due to air traffic, he is then told he must land in Raleigh. Find the distance he will travel.

Which Law would you use? (a)

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