Find the area of each triangle using the formula 𝓐 = ½ bh,&nb...

Question

Find the area of each triangle using the formula 𝓐 = ½ bh, and then verify that the formula 𝓐 = ½ ab sin C gives the same result.

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine the area of Chang ABC with the following measurements where A B is 36 centimeters. AC and BC are also 36 centimeters and angle B and angle C are 60 degrees. For our answer choices ass it's 324 multiplied by the square root of three square centimeters. B 324 square centimeters. C 648 multiplied by the square root of three square centimeters and D 648 square centimeters. Now, before we try to figure out the area of triangle ABC, let's try to figure out our missing an A. Now recall that in a triangle, the sum of angles is equal to 180 degrees. If angles B and C are 60 degrees, then that must mean angle A is also 60 degrees because 60 plus 60 plus 60 equals 180. That also makes sense because all the sides are 36 centimeters. So this is an equilateral triangle. Now, if we're going to find the area of triangle ABC, let's ask ourselves, what do we know about the area of triangles. Well, recall, OK, that the area of a triangle is equal to half of A B multiplied by the sine of anger C. In other words, what this is telling us is that to find the area of a triangle, we can multiply two sides and the sine of the anger between them by a half. Now, let's look at our triangle here. Do we know any pair of two sides and the anger between them? Well, yes, we do. In all cases, let's take an A, for example, for anger, A, we know the two sides that formed the angler 36 centimeters and angle A is 60 degrees. So using that idea, then the area for a triangle here, I'm gonna put that in red is going to be equal to a half of BC because each of these sides are opposite to angles B and C. So A half of BC multiplied by the sine of angle A. In this case, that's going to be a half of 36 multiplied by 36 multiplied by the sine of 60 degrees. No, when we put this into our calculator, OK. We should find that we get our answer to be 324 multiplied by the square root of three square centimeters. That would be the area of our triangle. Thus A is the correct answer. Thanks for watching everyone. I hope this video helps

Find the area of each triangle using the formula 𝓐 = ½ bh, and then verify that the formula 𝓐 = ½ ab sin C gives the same result.
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Key Concepts

Area of a Triangle

Trigonometric Functions

Verification of Area Formulas

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