Quiz about Law of Sines and Cosines Practice

Question 1

Set up the law of sines to find side AB.

Accepted Answer

$$\frac{\sin\left(53\right)}{AB}=\frac{\sin\left(44\right)}{7}$$

Answer

$$\frac{\sin\left(44\right)}{AB}=\frac{\sin\left(53\right)}{7}$$

Answer

$$\frac{\sin\left(AB\right)}{53}=\frac{\sin\left(7\right)}{44}$$

Answer

$$\frac{\sin\left(53\right)}{AB}=\frac{\sin\left(53\right)}{7}$$

Question 2

Find the angle at B.

Accepted Answer

29

Answer

35

Answer

209

Answer

87

Question 3

The angle at B is 29^o.

Set up the law of sines to find side BC.

Accepted Answer

$$\frac{\sin\left(93\right)}{BC}=\frac{\sin\left(29\right)}{16}$$

Answer

$$\frac{\sin\left(BC\right)}{93}=\frac{\sin\left(58\right)}{16}$$

Answer

$$\frac{\sin\left(29\right)}{BC}=\frac{\sin\left(93\right)}{16}$$

Answer

$$\frac{\sin\left(93\right)}{BC}=\frac{\sin\left(58\right)}{16}$$

Question 4

Solve the law of sines to find the length of side BC.

$$\frac{\sin\left(93\right)}{BC}=\frac{\sin\left(29\right)}{16}$$

Accepted Answer

$$BC=\frac{16\sin\left(93\right)}{\sin\left(29\right)}=32.96$$

Answer

$$BC=\frac{16\sin\left(29\right)}{\sin\left(93\right)}=7.8$$

Answer

$$BC=\sin^{-1}\left(\frac{16\sin\left(93\right)}{29}\right)=33.4$$

Question 5

Which equation could NOT be used to find x?

(Choose the equation that is set up incorrectly.)

Accepted Answer

$$\frac{x}{\sin\left(22.5\degree\right)}=\frac{97}{\sin\left(73.6\degree\right)}$$

Answer

$$\frac{x}{\sin\left(22.5\degree\right)}=\frac{121}{\sin\left(73.6\degree\right)}$$

Answer

$$\frac{x}{\sin\left(22.5\degree\right)}=\frac{97}{\sin\left(83.9\degree\right)}$$

Question 6

If a triangle has 1 angle and 2 sides, there are often two possible triangles. You solve law of sines to find the first possible angle for the triangle.

How do you find the second possible angle?

Accepted Answer

Subtract your first answer from 180^o

Answer

Subtract your first answer from 360^o

Answer

Add your first answer to 180^o

Answer

Subtract the angle on the triangle from your first answer

Question 7

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees.

Which equation can be used to find the angle opposite the side with length 31?

Accepted Answer

$$\frac{46}{\sin\left(53\degree\right)}=\frac{31}{\sin\left(x\right)}$$

Answer

$$\frac{46}{\sin\left(53\degree\right)}=\frac{x}{\sin\left(31\degree\right)}$$

Answer

$$\frac{46}{\sin\left(x\right)}=\frac{31}{\sin\left(53\degree\right)}$$

Answer

$$\frac{x}{\sin\left(53\degree\right)}=\frac{31}{\sin\left(46\degree\right)}$$

Question 8

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees.

Solve for x to find a possible measure of the angle opposite the side with length 31. (Round to the nearest degree.)

$$\frac{46}{\sin\left(53\degree\right)}=\frac{31}{\sin\left(x\right)}$$

Accepted Answer

$$x=\sin^{-1}\left(\frac{31\sin\left(53\right)}{46}\right)$$

Answer

$$x=\frac{31\sin\left(53\right)}{46}$$

Answer

$$x=\frac{46}{31\sin\left(53\right)}$$

Answer

$$x=\sin^{-1}\left(\frac{46}{31\sin\left(53\right)}\right)$$

Question 9

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees.

Find the possible measure(s) of the angle opposite the side with length 31. (Round to the nearest degree.)

$$\frac{46}{\sin\left(53\degree\right)}=\frac{31}{\sin\left(x\right)}$$

Accepted Answer

$$33\degree$$ and $$147\degree$$

Answer

$$33\degree$$ only

Answer

$$33\degree$$ and $$123\degree$$

Answer

$$33\degree$$ and $$213\degree$$

Question 10

Set up the law of cosines to find side XZ.

Accepted Answer

$$a^2=21^2+16^2-2\left(21\right)\left(16\right)\cos\left(139\right)$$

Answer

$$a=21^2+16^2-2\left(21\right)\left(16\right)\cos\left(139\right)$$

Answer

$$21^2=a^2+16^2-2\left(21\right)\left(16\right)\cos\left(139\right)$$

Question 11

Find side QR.

Accepted Answer

34.7 km

Answer

2.2 km

Answer

13.74 km

Answer

31.1 km

Question 12

Set up the law of cosines to find angle Z.

Accepted Answer

$$28^2=25^2+23^2-2\left(25\right)\left(23\right)\cos\left(z\right)$$

Answer

$$25^2=28^2+23^2-2\left(28\right)\left(23\right)\cos\left(z\right)$$

Answer

$$23^2=25^2+28^2-2\left(25\right)\left(28\right)\cos\left(z\right)$$

Question 13

Which equation could NOT be used to find x? (Choose the equation that is set up incorrectly.)

Accepted Answer

$$x^2=97^2+121^2-2\left(97\right)\left(121\right)\cos\left(73.6\degree\right)$$

Answer

$$x^2=97^2+121^2-2\left(97\right)\left(121\right)\cos\left(22.5\degree\right)$$

Answer

$$121^2=x^2+97^2-2\left(x\right)\left(97\right)\cos\left(73.6\degree\right)$$

Law of Sines and Cosines Practice

15 questions

Set up the law of sines to find side AB.

Find the angle at B.

The angle at B is 29^o.
Set up the law of sines to find side BC.

Which equation could NOT be used to find x?
(Choose the equation that is set up incorrectly.)

If a triangle has 1 angle and 2 sides, there are often two possible triangles. You solve law of sines to find the first possible angle for the triangle.
How do you find the second possible angle?

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees.
Which equation can be used to find the angle opposite the side with length 31?

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Law of Sines and Cosines Practice

15 questions

Set up the law of sines to find side AB.

Find the angle at B.

The angle at B is 29o.Set up the law of sines to find side BC.

Which equation could NOT be used to find x?(Choose the equation that is set up incorrectly.)

If a triangle has 1 angle and 2 sides, there are often two possible triangles. You solve law of sines to find the first possible angle for the triangle.How do you find the second possible angle?

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees.Which equation can be used to find the angle opposite the side with length 31?

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

The angle at B is 29^o.
Set up the law of sines to find side BC.

Which equation could NOT be used to find x?
(Choose the equation that is set up incorrectly.)

If a triangle has 1 angle and 2 sides, there are often two possible triangles. You solve law of sines to find the first possible angle for the triangle.
How do you find the second possible angle?

A triangle has side lengths 46 and 31. The angle opposite the side with length 46 measures 53 degrees.
Which equation can be used to find the angle opposite the side with length 31?