A real estate agent wants to find the area of...

Question

A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are 52.1 m and 21.3 m, and the angle between them is 42.2°. What is the area of the triangular lot?

Accepted Answer

Hello to day, we are going to be solving the following problem. So we are told that a triangular swimming pool will be constructed in hotel, two sides of the pool measure 10.5 m and 12.6 m. The angle between these sides is 58.1 degrees. We want to find the area of the swimming pool. Let's go ahead and draw a picture to help us solve this problem. So we know that the shape of the pole is going to be triangular. So we're going to draw a generic triangle. Next, we know that two sides of the pool have the measurements of 10.5 m and 12.6 m. We are also told that the angle between these two sides has a total of 58.1 degrees. How can we use this information to solve for the area of the triangle? While there's a special form of the area of the triangle which allows us to use the two sides and the angle measure if we label this side length A, this side length B and this side length C with the respective angles A B and C the area of the triangle that we can use is the area is equal to one half multiplied by a multiplied by C I mean, I'm sorry, multiplied by B multiplied by sine of the angle C. So now what we are going to do is we're going to plug in the two side links and the angle to solve for the area doing so will give us one half multiplied by side length A which is 10.5 m multiplied by s side length B which is 12.6 m multiplied by sine of angle C which is 58.1 degrees. Now one half multiplied by 10.5 multiplied by 12.6 is going to give us 66.15 m squared. And we are going to multiply this with sine of 58.1 degrees. At this point, I would recommend using a calculator to help you solve the product. After plugging the product into a calculator, you'll have a value of 56.16 m squared. And if we round to the to the one's place, we will have an approximate value of 56 m squared. This is going to be the area of the triangular pool. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are 52.1 m and 21.3 m, and the angle between them is 42.2°. What is the area of the triangular lot?

Key Concepts

Triangle Area Using Two Sides and Included Angle

Sine Function in Trigonometry

Angle Measurement in Degrees

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