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

## Example Questions

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

Use the Law of Cosines to find

(Triangle not drawn to scale.)

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

Use the Law of Cosines to find .

(Triangle not drawn to scale.)

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

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?

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

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 ?

Explanation:

Write the formula for the Law of Cosines.

Substitute the known values and solve for .

### Example Question #5 : Solve A Triangle In Which 2 Sides And An Included Angle Are Given (Sas)

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

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

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

Solve for . Round to the nearest tenth.

None of these answers are correct.