Precalculus : Solve a Triangle in Which 2 Sides and an Included Angle Are Given (SAS)

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #6 : Law Of Cosines

Use the Law of Cosines to find 

6

(Triangle not drawn to scale.)

Possible Answers:

Correct answer:

Explanation:

We need to use the Law of Cosines in order to solve this problem

in this case,  

In order to arrive at our answer, we plug the numbers into our formula:

Note: we use the "approximately" to indicate the answer is around 6.6. It will vary depending on your rounding.

Example Question #1 : Solve A Triangle In Which 2 Sides And An Included Angle Are Given (Sas)

Use the Law of Cosines to find .

7

(Triangle not drawn to scale.)

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to use the following formula

in this case, 

We plug our numbers into our formula and get our answer:

 

Note: we use the "approximately" to indicate that the answer is around 9.6. It will vary depending on your rounding.

Example Question #432 : Pre Calculus

The 2 sides of a triangle have lengths of 10 and 20.  The included angle is 25 degrees.  What is the length of the third side to the nearest integer?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the Law of Cosines.

Substitute the side lengths of the triangle and the included angle to find the third length.

Round this to the nearest integer.

Example Question #433 : Pre Calculus

What is the approximate length of the unknown side of the triangle if two sides of the triangle are  and , with an included angle of ?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the Law of Cosines.

Substitute the known values and solve for .

Example Question #2 : Solve A Triangle In Which 2 Sides And An Included Angle Are Given (Sas)

Lc1c

What is the measurement of side  using the Law of Cosines? Round to the nearest tenth.

Possible Answers:

Correct answer:

Explanation:

The Law of Cosines for side  is,

 .

Plugging in the information we know, the formula is,

 .

Then take the square of both sides: .

Finally, round to the appropriate units: .

Example Question #11 : Law Of Cosines

Use the Law of Cosines to solve for the specified variable.

Pcq1

Solve for . Round to the nearest tenth.

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

Law of Cosines

Therefore...

After rounding...

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