law of cosine trig

Question

Find the missing side or angle. Round to the nearest tenth.

b=26

a=25

c=5

B=?

Answer 1

The law of cosines:

c² = a² + b² − 2ab cos(C)

Note that the basis for the formula is that angle C is opposite side c. Therefore, simply relabel your given numbers, putting the "b" value in place of c. (The order of the other two does not matter)

So, using your given numbers:

26² = 25² + 5² - 2(25)(5)*cos(B)

Solve this for B

Answer 2

The law of cosines says that b² = a² + c² - 2ac*cos(B)

Have you tried using it? Where are you getting stuck?

Answer 3

Grace, we have to make sure our variables are defined. That is the reason many students have difficulty. They remember things like a^2 + b^2 = c^2 without attaching a, b and c to the right geometric meanings.

Let us suppose that we are given a triangle ABC with vertices A, B and C and sides little a, b and c, opposite the corresponding lettered vertices.

We know little a, little b and little c and want the measure of angle big B. In this case we can use the law of cosines which tells us that in this case:

b^2 = a^2 + c^2 - 2ac*cos(B); note that angle B is between side a and side c. We can solve this for cos(B).

b^2 - a^2 - c^2 = -2ac*cos(B)

(b^2 - a^2 - c^2)/(-2ac) = cos(B)

Now we can take the inverse cosine of both sides:

cos^-1[(b^2 - a^2 - c^2)/(-2ac)] = cos^-1[cos(B)] = B

so B = cos^-1[(b^2 - a^2 - c^2)/(-2ac)] = cos^-1[(26^2 - 25^2 - 5^2)/(-2* 25 * 5)] = cos^-1(-.104) = 95.96956 degrees is approximately 96.0 degrees, rounded to the nearest tenth of a degree.