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.

B = 125°, a = 8 yards, c = 5 yards

Accepted Answer

Hey, everyone in this problem, we're asked to determine the area of triangle ABC where angle B is equal to 136 degrees. Side A is 10 centimeters and side C is seven centimeters. We're told to write our answer to the nearest integer. We have four answer choices all in centimeters squared. Option A 25 option B 24 option C 97 option D 49. So the first thing we want to think about is how these angles and sides are related. OK. If we draw our triangle, are they opposite sides, are they adjacent sides? What does this look like? So we're gonna draw a quick little triangle and this is not to skin does not necessarily what this triangle is going to look like. But again, we just want these relationships. So at the top, we're gonna draw angle B, OK. And we know that if we have angle B, then the side across from angle B will be side B. OK. That is how we label triangles. What that means is that the two sides were given A and C are gonna be adjacent to angle B that we were given. OK. So we have A and C, we've drawn a on the left and C on the right in our diagram, but they could be the opposite. What's important here is that again, we have two adjacent sides with that enclosed angle and these three all at the top. So in a situation like this, we want to recall that the area is gonna be equal to the product of the two sides we were given. So in this case, a multiplied by C divided by two multiplied by sign of that enclosed angle. In this case, B substituting in our values, we have that the area is gonna be 10 centimeters multiplied by seven centimeters divided by two multiplied by sine of degrees. And if we work this out on our calculator, we get that the area is gonna be 24. centimeters squared. And that is that area we were looking for. And that's a really neat result. OK? You don't know any information about the third side links. We don't know anything about these additional angles. But knowing that one angle in those two side links allow us to calculate this area. OK. If we round to the nearest integer, we can see that this corresponds with answer choice B 24 centimeters squared. That's it for this one. Thanks everyone for watching. I hope this video helped.

In Exercises 33–38, find the area of the triangle having the given measurements. Round to the nearest square unit. B = 125°, a = 8 yards, c = 5 yards

Key Concepts

Law of Sines

Area of a Triangle

Triangle Properties

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