# Precalculus : Find the Area of a Triangle When Given One Side and Two Angles, Or When Given Two Sides and An Included Angle

## Example Questions

### Example Question #1 : Area Of A Triangle

In triangle , , , and .  Find the area of the triangle.

Explanation:

When given the lengths of two sides and the measure of the angle included by the two sides, the area formula is:

Plugging in the given values we are able to calculate the area.

### Example Question #1 : Find The Area Of A Triangle When Given One Side And Two Angles, Or When Given Two Sides And An Included Angle

Find the area of this triangle:

Explanation:

To find the area, use the formula associated with side, angle, side triangles which states,

where  and  are side lengths and  is the included angle.

In our case,

.

Plug the values into the area formula and solve.

### Example Question #3 : Find The Area Of A Triangle When Given One Side And Two Angles, Or When Given Two Sides And An Included Angle

Find the area of this triangle:

Explanation:

Use the area formula to find area that is associated with the side angle side theorem for triangles.

where  and  are side lengths and  is the included angle.

Plugging these values into the formula above, we arrive at our final answer.

### Example Question #4 : Find The Area Of A Triangle When Given One Side And Two Angles, Or When Given Two Sides And An Included Angle

Find the area of this triangle:

Explanation:

To solve, use the formula for area that is associated with the side angle side theorem for triangles,

where  and  are side lengths and  is the included angle.

Here we are using and not since that is the angle between  and .

Therefore,

.

Plugging the above values into the area formula we arrive at our final answer.

### Example Question #2 : Find The Area Of A Triangle When Given One Side And Two Angles, Or When Given Two Sides And An Included Angle

Find the area of this triangle:

Explanation:

Find the area using the formula associated the side angle side theorem of a triangle,

where  and  are side lengths and  is the included angle.

In this particular case,

therefore the area is found to be,

.