This word problem involves finding the perimeter of a trapezoid by creating a right triangle in the trapezoid and using the trig functions in order to find a missing side. Once you find the missing side you can add of the sides together in order to find the perimeter.
How do you find the angle measure of a right triangle using trig functions? Follow these steps.
Step 1.From the unknown angle, decide which two sides you have. By evaluating which angles you have you can decide which trig function to use.( Sin,Cosine,Tangent)
For example if I have opposite and hypotenuse I'm going to use the sin function.
Step. 2.After deciding which trig function to use, set up the problem, and instead of the variable being x in the proportion the variable will be at the angle.
30-60-90 Triangles are one type of special triangles. They
are important for many students because the SAT and Act ask several questions
involving this special right triangle. Here are 7 helpful resources you can use
to master the 30-60-90 triangle.
Free Math Help This page has several examples that
demonstrate the relationship between the side lengths, and the angle measure of
30-60-90 triangles.
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Grade A Math This page does a great job of explaining how to
find the missing sides of a 30 60 90 along with several example problems.
30-60-90 Right Triangle by radical prep. This video has
55,000 views on YouTube. It works several SAT type problems that involve a
30-60-90 triangle, and why it is important to memorize the ratio of the sides.
45-4-90 and 30-60-90 Triangles In this video by Patrick of JMT, he explains the
difference between a 45-45-90 triangle, and a 30-60-90 triangle. This video is
very helpful, very clear, and he has a very relaxed style.
30-60-90 Triangle MooMooMath This page has a helpful review
of the characteristics of a 30-60-90 triangle, along with several shortcuts to use
when finding side length.
Special right triangle song. I love this video. The song is
not great, but the lyrics stick in your head, and it can really you help memorize
the properties of special right triangles. The lyrics are included in the
video description.
Finally, here are two helpful calculators that will
calculate the side length of a 30-60-90 triangle. Calculators are handy in order to check your homework. I looked at several
calculators and felt these are the easiest to use.
Enjoy this quick reference infographic on Pythagorean Theorem word problems. The Pythagorean Theorem is used with right triangles in order to find missing sides and angles. As a result it can be applied to many different situations. Each of these word problems has a video answer that explains how they are solved.
If you enjoy this infographic please share or embed.
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Video of the day Sine, Tangent, Cosine
In this video you will learn……
How to set up the ratio for sine
How to set up the ratio for cosine
Sine equals Opposite over hypotenuse
Cosine equals adjacent over hypotenuse
Learn how to decide which side is opposite and which side is adjacent
Learn which side of the triangle is always the hypotenuse
Watch sample problems that involve setting up sine and cosine
For more information see Sine,Tangent,Cosine
Today we are going to look at applying the Pythagorean Theorem. So here is our example problem. A 12 foot ladder is placed four feet from the base of a wall. How far up the wall will the ladder reach? I'm going to start with the rules of working with a word problems in Geometry. So here are the rules, the first rule is that you always draw a picture. Get out your marker and draw a scenario of what this situation looks like. Then I want you to label it. Take all the information and label the picture, and since this is the Pythagorean Theorem. We will identify where is A where is B and where is C and then we will plug everything we do know into the Pythagorean Theorem and solve for the unknown. So let’s go through the steps. Let’s draw a picture. We have a wall and we have a ladder leaning against the wall. (Draws this) and now let’s label what we know. We know this is a 12 foot ladder and it is placed four feet from the base of the wall. So that means my four feet is here. (points to bottom of triangle) and I have the right angle here. Now opposite the right angle is the hypotenuse or C that means the floor is B so A is missing. I have now identified A, B, and C. So now we are going to apply the Pythagorean Theorem.A squared plus B squared plus C squared. So I will plug in 4 for B and 12 for C and I’m going to have to solve for A. So let’s square these out. four squared is 16, and 12 squared is 144 and I don’t know my A squared. Now let’s subtract 16 from both sides. So 144 minus 16 is 128 is equal to A squared. To undo a square you take the square root so the square root of 128, so to find the square root of 128 I will make a factor tree. So 2 times 64 and 64 is a perfect square (square root of 64 is 8) so I take my pair out 8 square root 2 so that is how long A is. You could also get the decimal version by originally taking the square root of 128 on your calculator, but the exact answer is 8 square 2. Hope this was helpful.
MooMooMath provides short Math video clips to help you with your Math homework. We also have a summary of each clip along with example problems. The videos are produced by veteran teachers that have over twenty years teaching experience. We have clips in Geometry, Trigonometry, and Algebra. Please visit our You Tube Channel or website to see all of our videos
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