A painter is going to apply paint to a triangular metal plate ...

Question

A painter is going to apply paint to a triangular metal plate on a new building. Two sides measure 16.1 m and 15.2 m, and the angle between the sides is 125°. What is the area of the surface to be painted?

Accepted Answer

Hello to day. We are going to be solving the following word problem. So we are told that Diane is going to cut cards into triangular shapes which will be used as decorations for a birthday party. Two sides of the triangle have the lengths of 12.3 centimeters and 15.7 centimeters. If the angle between these sides is 98 degrees, what is the area of each triangular carding? So the problem tells us that we are dealing with triangular shapes. Let's go ahead and draw a general triangle. We're going to label the side links A B and C S length A will have the respective angle. A sil length B will have the respective angle B and S length C will have the respective angle C. Now, we are told that two of these side links is going to be 12.3 centimeters and 15.7 centimeters. We will let angle or side length a be 12.3 centimeters and we will let side length be be 15.7 centimeters. We are also told that the angle between these two sides is 98 degrees. That angle is going to be the angle C. So how can we use this information to find the area of this triangle? Well, notice that the problem gives us the measures of two side links and an angle there is a special form for the area of the triangle that lets us find the area. As long as we are given two side links and an angle, the area is equal to one half multiplied by the two side lengths, which is going to be side length. A multiplied by side length B multiplied by sine of the angle which in this case is going to be angle C. So we are going to use this formula of the area to calculate the area of a triangle. So plugging in the values, we will have one half multiplied by side length A which is 12.3 centimeters multiplied by side length B which is 15.7 centimeters multiplied by sine of the given angle which is 98 degrees, one half multiplied by 12.3 multiplied by 15.7 will give us the decimal 96.56 centimeters squared. And we are multiplying this value by sign of 98 degrees. I would recommend using a calculator to help you multiply these values together. And when plugging in this product into a calculator, we will end up with an area of 95.62 centimeters squared, which will estimate to be exactly 96 centimeters squared. This is going to be the area of the triangular shaped cutouts that Diane will make. And with that being said, the answer to this problem is going to be c 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 painter is going to apply paint to a triangular metal plate on a new building. Two sides measure 16.1 m and 15.2 m, and the angle between the sides is 125°. What is the area of the surface to be painted?

Key Concepts

Law of Cosines for Area Calculation

Sine Function in Trigonometry

Triangle Area Calculation

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