Question

PLEASE HELP!!!! A triangle has sides of lengths a=17, b=36, c=45 km.

Find the measures of the 3 angles
Enter your answer as a number; answer should be accurate to 2 decimal places.

Angle A =____?
Angle B = ____?
Angle C = ____?

Explain how you found the 3 angles below. Be sure to show all of your work.

Answer 1

Answers:

• Angle A = 20.64 degrees
• Angle B = 48.29 degrees
• Angle C = 111.07 degrees

You may or may not have to type in the word "degrees", and/or use the degree symbol. I would ask your teacher for clarification.

A diagram is shown below.

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Step-by-step explanation:

We'll need the law of cosines to solve for angle A.

a^2 = b^2 + c^2 - 2*b*c*cos(A)

17^2 = 36^2 + 45^2 - 2*36*45*cos(A)

289 = 3321 - 3240*cos(A)

289 - 3321 = -3240*cos(A)

-3032 = -3240*cos(A)

-3240*cos(A) = -3032

cos(A) = (-3032)/(-3240)

cos(A) = 0.935802

A = arccos(0.935802)

A = 20.64 degrees

which is approximate to 2 decimal places.

Note: The "arccos" refers to "arccosine" which is the same as inverse cosine (denoted as
`\cos^(-1)` on many calculators).

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Do a similar set of steps for angle B.

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

36^2 = 17^2 + 45^2 - 2*17*45*cos(B)

1296 = 2314 - 1530*cos(B)

1296 - 2314 = -1530*cos(B)

-1018 = -1530*cos(B)

-1530*cos(B) = -1018

cos(B) = (-1018)/(-1530)

cos(B) = 0.665359

B = arccos(0.665359)

B = 48.29 degrees

Also approximate to 2 decimal places.

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As you can probably guess by now, we could use the law of cosines to find angle C. But a much quicker shortcut is to use the fact that for any triangle, the interior angles always add to 180 degrees.

This shortcut is only possible since we know the two other angles.

Solve for C.

A+B+C = 180

C = 180-A-B

C = 180 - 20.64 - 48.29

C = 111.07 degrees

Like the others, this is approximate to 2 decimal places.

You can use a graphing tool like GeoGebra to confirm the answers. See below. Due to the SSS (side side side) triangle congruence theorem, only one triangle is possible. This means only one answer is possible per angle.