𝐴𝐵𝐶 is a triangle, where 𝐴𝐵 is equal to five centimeters, 𝐴𝐶 is equal to 11 centimeters, and the measure of the angle at 𝐴 is 107 degrees. Find the area of the triangle giving the answer to two decimal places.
It’s very tricky to work out what you need to do here without drawing a diagram. Remember, this just needs to be a sketch and therefore does not need to be to scale.
Now we have sketched this out, we can see that we have a nonright-angled triangle for which we need to find the area. Let’s recall the formula for finding the area of a nonright-angled triangle.
The area is equal to a half 𝑎𝑏 sin 𝐶. Remember, we label the sides of our triangle with a lower case letter. This letter corresponds to the letter of the vertex the side is opposite to. You’ll notice we switched capital 𝐴 with capital 𝐶.
The formula for our area has the angle marked as 𝐶. Therefore, it’s easier to change the name of our angle in our diagram to capital 𝐶. Once we’ve done this, it’s simply a case of substituting the values we now know into our formula for the area of the triangle.
The area is equal to a half times fives times 11 times sin 107. This give us a value of 26.298. The area of the triangle is 26.30 centimeters squared, correct to two decimal places.