You Try It

Now it's your turn to try solving some problems. Work through the problems and questions on the tabs below, before clicking the Answer buttons to check your work. Remember to decide before starting the problem which Law of Cosines formula will work best.

Problem 1

Problem 2

Problem 3

Find the measure of side a for the triangle below.

Triangle

We are given the following information:

m∠A = 114°
b = 23
c = 26

We already have an image of the triangle.

Triangle

Now we need to pick the right formula and solve for side a.

a² = b² + c² - 2bc cos(A)
a² = 23² + 26² - 2(23)(26) cos(114°)
a² = 529 + 676 - (-486.5)
a² = 1691.5
a ≈ 41.1

Triangle ABC has the following side measures.

a = 25
b = 23
c = 14

Find the measure of angle C.

We are given the measures of the three sides of an oblique triangle. We can draw the following picture:

Triangle

Since we need to solve for angle C we can use the following formula.

c² = a² + b² - 2ab cos(C)
14² = 25² + 23² - 2(25)(23)cos(C)
196 = 625 + 529 - 1150cos(C)
196 = 1154 - 1150cos(C)
-958 = -1150cos(C)
0.833 = cos(C)
C = cos^-1(0.833)
C ≈ 33.6°

Find the measure of side b for the triangle below.

Triangle

We are given the following pieces of information about the triangle:

a = 11
c = 15
m∠B = 116°

Now we can choose the right formula and solve for side b.

b² = a² + c² - 2ac cos(B)
b² = 11² + 15² -2(11)(15)cos(116°)
b² = 121 + 225 - 330cos(116°)
b² = 121 + 225 - (-144.7)
b² = 490.7
b ≈ 22.2

Can you figure out a solution to these problems?