Video Transcript
๐ด๐ต๐ถ is a triangle, where ๐ด๐ต is equal to five centimeters, ๐ด๐ถ is equal to 11 centimeters, and the measure of the angle at ๐ด is 107 degrees. Find the area of the triangle giving the answer to two decimal places.
Itโs 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. Letโs recall the formula for finding the area of a nonright-angled triangle.
The area is equal to a half ๐๐ sin ๐ถ. 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. Youโll notice we switched capital ๐ด with capital ๐ถ.
The formula for our area has the angle marked as ๐ถ. Therefore, itโs easier to change the name of our angle in our diagram to capital ๐ถ. Once weโve done this, itโs 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.
