To find the area of a triangle with two sides of length 5 and 9 and the included angle of 78 degrees, you can use the following formula for the area of a triangle:
Area = (1/2) * a * b * sin(C)
Where:
- "a" and "b" are the lengths of the two sides.
- "C" is the included angle between those two sides.
- "sin" represents the sine function, which you should use in degrees.
In this case:
- "a" is 5
- "b" is 9
- "C" is 78 degrees
Now, plug these values into the formula:
Area = (1/2) * 5 * 9 * sin(78°)
Calculate the sine of 78 degrees:
sin(78°) ≈ 0.978
Now, calculate the area:
Area ≈ (1/2) * 5 * 9 * 0.978 ≈ 21.951 square units
So, the approximate area of the triangle is 21.951 square units.