Name: Trigonometry Word Problems- Perimeter of a Trapezoid | Videos | Gan Jing World - Technology for Humanity | Video & Movie Streaming
Uploaded: 2023-12-01T23:26:22.993Z
Duration: 5 min 41 s
Description: Trig Word Problems-Perimeter of a Trapezoid This word problem involves finding the perimeter of a t... | Videos | Gan Jing World - Technology for Humanity | Video & Movie Streaming

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Trig Word Problems-Perimeter of a Trapezoid

This word problem involves finding the perimeter of a trapezoid by creating a right triangle, and using the trig functions in order to find a missing side. 

Transcript

Now lets jump into some that you will see that are multi step problems you will see on the ACT. Let me sketch it up here. Find the perimeter of Trapezoid ABCD. 
Why are we looking at the perimeter of a trapezoid in a trig unit? I will show you why. We need to find the perimeter. We don't know the two sides so we are going to do something to find these missing sides. Watch what I will do. I'm going to draw in an altitude. I will make this into a rectangle on the left. If I draw this in, what do I know this measurement is? That measurement is 2. I don't know this measurement, but I do know this measurement of the height has to be 8. Now I can solve for one of two sides. I can solve for the hypotenuse of the triangle, or solve for the leg of the triangle. Lets focus on the triangle. I'm going to go for the hypotenuse first. I will take the side of 8, which is my opposite, and the unknown side of C, and I will solve. It will be opposite over hypotenuse which is sine. So I have the sine of 54 = 8/c. Grab your calculator and the sine of 54 = .809C and divide both sides by .8090 and that equals 9.8887 or 9.9 c. I'm not done yet. I still have a missing segment. This time I have a choice. Because I have a right triangle and I know two sides. I can use the Pythagorean Theorem and solve for the missing side. Option 1 is use the Pythagorean Theorem and solve for the missing side.
Option 2 Use another trig function. 
Use 8 and the adjacent side and use tangent.
I'm using the Pythagorean Theorem  because it is easier for me or you can use a trig function. a^2 + b^2 = c^2 = 9.9^2
which equals 98 = 64 + a^2 and I will get a^2 = 34 and take the square root of 34 which equals 5.8 , so that is a.
From here I can now I can find the perimeter. Because I can add all the sides together. This whole side is 7.8, annd the side lengths of the trapezoid are 9.9,2 , and 8. I need the altitude of 8. I will all the sides together and I get 2+9.9 + 7.8 = 27.7 
The perimeter is 27.7 and that is how I use trig and the Pythagorean theorem to find the perimeter of the trapezoid.

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Trigonometry Word Problems- Perimeter of a Trapezoid

MooMooMath and Science

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