Precalculus : Solve a Triangle in Which 3 Sides Are Given (SSS)

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #32 : Trigonometric Applications

Which is NOT an angle of the following triangle?


(Not drawn to scale.)

Possible Answers:

Correct answer:


In order to solve this problem, we need to find the angles of the triangle. Only then will we be able to find which answer choice is NOT an angle. Using the Law of Cosines we are able to find each angle.



To find angle  we use the formula again or we can remember that the angles in a triangle add up to .



The answer choice that isn't an actual angle of the triangle is .

Example Question #33 : Trigonometric Applications

Solve the triangle



Possible Answers:

None of the other answers

Correct answer:


Since we are given all 3 sides, we can use the Law of Cosines in the angle form:

Let's start by finding angle A:

Now let's solve for B:

We can solve for C the same way, but since we now have A and B, we can use our knowledge that all interior angles of a triangle must add up to 180 to find C.

Example Question #34 : Trigonometric Applications

Given three sides of the triangle below, determine the angles , and  in degrees.


Possible Answers:

Correct answer:


We are only given sides, so we must use the Law of Cosines. The equation for the Law of Cosines is


where  and  are the sides of a triangle and the angle  is opposite the side .

We have three known sides and three unknown angles, so we must write the Law three times, where each equation lets us solve for a different angle. 

To solve for angle , we write

 and solve for  using the inverse cosine function  on a calculator to get


Similarly, for angle ,

and for ,



Example Question #35 : Trigonometric Applications


What is the measurement of ? Round to the nearest tenth, if needed.

Possible Answers:

Correct answer:


We need to use the Law of Cosines for side  then solve for .



Plugging in the information provided, we have:


Then simplify, .

To solve for , use .

Solve and then round to the appropriate units: . Therefore, .

Example Question #1 : Law Of Cosines

Find the measure, in degrees, of the largest angle in a triangle whose sides measure , , and .

Possible Answers:

Correct answer:


When all three sides are given, Law of Cosines is appropriate. 

Since 10 is the largest side length, it is opposite the largest angle and thus should be the c-value in the equation below.

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