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.

A = 22°, b = 20 feet, c = 50 feet

Accepted Answer

Hey, everyone in this problem, we're asked to determine the area of triangle ABC where angle A is equal to 34 degrees. Side B is equal to 18 centimeters and side C is equal to centimeters. And a writer answer to the nearest integer, we're given four answer choices all in centimeters squared. Option A is 327. Option B is 328. Option C is 654 and option D is 1309. So the first thing we wanna do here is we're gonna draw a little sketch of this triangle and it's not gonna be to scale. It's not necessarily what this triangle looks like. But what we want to do is figure out the relationship between this angle we're given in these sides. OK? Where are they located relative to each other? So we're gonna say that this angle at the top of our triangle is angle A and recall it when you label triangles, if we have angle A, then the opposite side to that angle is going to be side A. OK. So we have angle A at the top here side A at the bottom. What that means is that the other two sides on either side of angle bay are gonna be B and C and they could be the opposite. We could have B on the right and C on the left. But what's important here is that we have two adjacent sides and an enclosed angle and all three of the values that we're given are up here and are together. Now, if we have two adjacent sides in an enclosed angle, we're called that the area of the triangle is gonna be given by the product of the two sides. We know be multiplied by C divided by two, multiplied by sign of that enclosed angle. In this case, sign of A, we know B we know C we know angle A, let's substitute all these values in to find the area. So we have that the area is gonna be 18 centimeters multiplied by 65 centimeters divided by two. And all of this is multiplied by a sine of 34 degrees. If we work this out on our calculator, we find that the area is gonna be 327. centimeters squared approximately. And we can round to the nearest integer like the question is asking and we'll get 327 centimeters squared, which corresponds with answer choice A, 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. A = 22°, b = 20 feet, c = 50 feet

Key Concepts

Law of Cosines

Area of a Triangle

Sine Function

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