In Exercises 33–38, find the area of the triangle having the give...

Question

In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit.

C = 102°, a = 16 meters, b = 20 meters

Accepted Answer

Everyone in this problem, we're asked to determine the area of triangle ABC with the following measurements and to write our answer to the nearest integer. OK. We're told that C is equal to 113 degrees. Little A is equal to 13 inches and little B is equal to 30 inches. We're given four answer choices all in square inches. Option A 180 option B option C 718 and option D 179. All right. So let's think about what we are given here. We're gonna draw a little triangle and this is not gonna be to scale at all, but just to get a sense of where these angles and sides are in relation to each other, right? So we're told information about angle C, we're gonna draw that on our top angle and we know that if we have angle C then side C is opposite. OK. So these sides, we're given A and B are gonna be on either side of our angle seat. OK? They could be opposite, it could be B on the left and A on the right. We're not sure, but we know that each of those are gonna be A or B. What's important here is that we have two adjacent sides and the enclosed angle. When we have a situation like that recall that we can write the area of this triangle as the sum or product, sorry, of the two sides. A multiplied by B divided by two multiplied by sign of the angle we were given C so substituting in our values, we get that the area is gonna be 13 inches multiplied by 30 inches divided by two, multiplied by a sine of 113 degrees. And if we work this out on a calculator, we're gonna find that the area is approximately equal to 179.49, 85 square inches. OK. Rounding to the nearest integer. Like the problem asked us to do, we're gonna round down and we get 179 square inches which corresponds with answer choice D. That's it for this one. Thanks everyone for watching. See you in the next video.

In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit. C = 102°, a = 16 meters, b = 20 meters

Key Concepts

Law of Cosines

Area of a Triangle

Trigonometric Functions

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