Question Icon

Hotmath Practice Problems

book image
Title:
Hotmath Algebra 2
Author:
Hotmath Team
 
Free
Chapter:TrigonometrySection:Law of Sines and Law of Cosines
 

Problem: 1

Check if the given measurements can form exactly one triangle, exactly two triangles, or no triangle.

mA = 70 , a = 165, c = 170

(Here A is the angle opposite side a, B is the angle opposite side b, etc.)


Problem: 3

Check if the given measurements can form exactly one triangle, exactly two triangles, or no triangle.

mB = 115 , b = 13, a = 7

(Here A is the angle opposite side a, B is the angle opposite side b, etc.)


Problem: 5

In ΔABC, determine the value of a if b = 5.50, mA = 105 , and mC = 65 to three significant digits.

(Here A is the angle opposite side a, B is the angle opposite side b, etc.)


Problem: 7

In ΔABC, determine mB if a = 6, b = 5, mA = 70 to three significant digits.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 9

In ΔABC, determine mC if a = 6, c = 9, mA = 39 to three significant digits.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 11

Solve for the unknown value x:


Problem: 13

Determine the value of unknown x.


Problem: 15

Use the Law of Sines to solve for x. Round to the nearest tenth.


Problem: 17

Use the Law of Sines to solve for x. Round to the nearest tenth.


Problem: 19

Write the correct form of the Law of Sines or the Law of Cosines to solve for q.


Problem: 21

Write the correct form of the Law of Sines or the Law of Cosines to solve for q.


Problem: 23

In ΔABC, Determine the value of c if a = 8, b = 9, mC = 40 of ΔABC. Determine the length to three significant digits.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 25

Consider ΔABC with the following measures:

a = 5

b = 12

C = 90

Find c using Law of Cosines.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 27

Determine mB if a = 14, b = 15, c = 17 of ΔABC. Determine the angle to the nearest tenth of a degree.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 29

Determine the smallest angle if a = 15, b = 25, c = 27 of ΔABC. Determine the angle to the nearest tenth of a degree.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 31

Determine the largest angle if a = 3.2, b = 2.9, c = 3.8 of ΔABC. Determine the angle to the nearest tenth of a degree.

(Here A is the angle opposite side a, B is the angle opposite side b, etc.)


Problem: 1

Check if the given measurements can form exactly one triangle, exactly two triangles, or no triangle.

mA = 70, a = 165, c = 170

(Here A is the angle opposite side a, B is the angle opposite side b, etc.)


Problem: 3

Check if the given measurements can form exactly one triangle, exactly two triangles, or no triangle.

mB = 115, b = 13, a = 7

(Here A is the angle opposite side a, B is the angle opposite side b, etc.)


Problem: 5

In ΔABC, determine the value of a if b = 5.50, mA = 105, and mC = 65 to three significant digits.

(Here A is the angle opposite side a, B is the angle opposite side b, etc.)


Problem: 7

In ΔABC, determine mB if a = 6, b = 5, mA = 70 to three significant digits.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 9

In ΔABC, determine mC if a = 6, c = 9, mA = 39 to three significant digits.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 11

Solve for the unknown value x:


Problem: 13

Determine the value of unknown x.


Problem: 15

Use the Law of Sines to solve for x. Round to the nearest tenth.


Problem: 17

Use the Law of Sines to solve for x. Round to the nearest tenth.


Problem: 19

Write the correct form of the Law of Sines or the Law of Cosines to solve for q.


Problem: 21

Write the correct form of the Law of Sines or the Law of Cosines to solve for q.


Problem: 23

In ΔABC, Determine the value of c if a = 8, b = 9, mC = 40 of ΔABC. Determine the length to three significant digits.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 25

Consider ΔABC with the following measures:

a = 5

b = 12

C = 90

Find c using Law of Cosines.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 27

Determine mB if a = 14, b = 15, c = 17 of ΔABC. Determine the angle to the nearest tenth of a degree.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 29

Determine the smallest angle if a = 15, b = 25, c = 27 of ΔABC. Determine the angle to the nearest tenth of a degree.

(Here A is the angle opposite side a,B is the angle opposite side b, etc.)


Problem: 31

Determine the largest angle if a = 3.2, b = 2.9, c = 3.8 of ΔABC. Determine the angle to the nearest tenth of a degree.

(Here A is the angle opposite side a, B is the angle opposite side b, etc.)