Video: Calculating the Area of a Triangle Using Sine

In the given figure, work out the area of the triangle to 2 decimal places.

01:15

Video Transcript

In the given figure, work out the area of the triangle to two decimal places.

In this figure, we were given two side lengths and an included angle. Since we have this information, we can use the formula 𝐴 equals one-half times 𝑎𝑏 times sin of 𝐶 to find the area, where 𝑎 and 𝑏 are side lengths and 𝐶 is an included angle. The area of this triangle is found by one-half times 10 times seven times sin of 136 degrees. If you plug this into your calculator, you get 24.3130429 continuing. If your calculator did not give you this answer, you should check and make sure that your calculator is set to degree mode and not to radians.

To get our final answer, though, we want it rounded to two decimal places. There’s a one in the second decimal place. To the right of that, in the third decimal place, the thousandths place, is a three. This means we should round down to 24.31. We weren’t given any units, so we can just say that the area of this triangle is 24.31 units squared.

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