# Video: Trigonometric Formulas for Area of Triangles

Which of the following is a formula that can be used to find the area of a triangle? [A] 1/2 ππ Cos πΆ [B] 1/2 ππ Sin πΆ [C] 1/3 ππ Sin πΆ [D] 1/4 ππ Cos πΆ [E] 1/4 ππ Sin πΆ

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### Video Transcript

Which of the following is a formula that can be used to find the area of a triangle? A) one-half ππ cos πΆ, B) one-half ππ sin πΆ, C) one-third ππ sin πΆ, D) one-fourth ππ cos πΆ, or E) one-fourth ππ sin πΆ.

If we sketch a triangle and label it π΄, π΅, and πΆ, the side length opposite vertex π΄ is usually labelled with a lower case π. The side length opposite vertex π΅ is labelled with a lower case π. And we label lower case π the side length opposite vertex πΆ. We have to remember that a triangle is half of a rectangle. And so, itβs unlikely that options C through E would be the answer.

We noticed that options A and B are dealing with the angle at vertex πΆ, thatβs this angle, and the lengths π and π. At this point, we recognize that we have two sides and an included angle. And we know that the height of this triangle will be equal to π times the sin of πΆ. To use trigonometry to solve for the area of a triangle, we take one-half times π times π times sin of πΆ, which is option B here.