Question Video: Using the Trigonometric Formula for Area of Triangles to Find the Area of a Triangle | Nagwa Question Video: Using the Trigonometric Formula for Area of Triangles to Find the Area of a Triangle | Nagwa

# Question Video: Using the Trigonometric Formula for Area of Triangles to Find the Area of a Triangle Mathematics • First Year of Secondary School

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๐ด๐ต๐ถ is a triangle where ๐ด๐ต = 5 cm, ๐ด๐ถ = 11 cm and ๐โ ๐ด = 107ยฐ. Find the area of the triangle giving the answer to two decimal places.

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### Video Transcript

๐ด๐ต๐ถ is a triangle, where ๐ด๐ต is equal to five centimeters, ๐ด๐ถ is equal to 11 centimeters, and the measure of the angle at ๐ด is 107 degrees. Find the area of the triangle giving the answer to two decimal places.

Itโ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. Letโs recall the formula for finding the area of a nonright-angled triangle.

The area is equal to a half ๐๐ sin ๐ถ. 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. Youโll notice we switched capital ๐ด with capital ๐ถ.

The formula for our area has the angle marked as ๐ถ. Therefore, itโs easier to change the name of our angle in our diagram to capital ๐ถ. Once weโve done this, itโ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.

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