## Geometry: How to use SOH CAH TOA

Welcome back to Mathsux! This week, we’re going to go over how to find missing angles and side lengths of right triangles by using trigonometric ratios (sine, cosine, and tangent).  Woo hoo! These are the basics of right triangle trigonometry, and provides the basis for mastering so many more interesting things in trig! So, let’s get to it!

Also, if you have any questions about anything here, don’t hesitate to comment below. Happy calculating! 🙂

Trigonometric Ratios (more commonly known as Sine, Cosine, and Tangent) are ratios that naturally exist within a right triangle.  This means that the sides and angles of a right triangle are in proportion within itself.  It also means that if we are missing a side or an angle, based on what we’re given, we can probably find it!

Let’s take a look at what Sine, Cosine, and Tangent are all about! Now let’s see how we can apply trig ratios when there is a missing side or angle in a right triangle!     Now for another type of question; using trig functions to find missing angles, let’s take a look:     Try the following Practice Questions on your own! Solutions: Still got questions?  No problem! Check out the video the same examples outlined above and happy calculating! 🙂

## Geometry: Median of a Trapezoid Theorem

*If you haven’t done so, check out the video that goes over this exact problem, also please don’t forget to subscribe!  Step 1:  Let’s apply the Median of a Trapezoid Theorem to this question!  A little rusty?  No problem, check out the Theorem below.

Median of a Trapezoid Theorem: The median of a trapezoid is equal to the sum of both bases. Step 2: Now that we found the value of x , we can plug it back into the equation for median,  to find the value of median  Want more practice?  Your wish is my command! Check out the practice problems below:

Practice Questions:

1. is the median of trapezoid ABCDEF, find the value of the median, given the following: 2. is the median of trapezoid ACTIVE, find the value of the median, given the following: 3. is the median of  trapezoid DRAGON, find the value of the median, given the following: 4. is the median of trapezoid MATRIX, find the value of the median, given the following: Solutions: Need more of an explanation?  Check out the detailedand practice problems. Happy calculating! 🙂

## Algebra: Completing the Square

Learn how to Complete the Square by clicking on the Youtube video and trying the practice problems below. Happy Calculating! 🙂

Click the picture below to view the Youtube video.  Practice Questions: Solutions: Need more of an explanation?  Check out why we complete the square in the first place here and please don’t forget to subscribe! 🙂

## Geometry: Area of a Sector Hi math friends, has anyone been cooking more during quarantine?  We all know there is more time for cookin’ and eatin’ cakes but have you ever been curious about the exact amount of cake you are actually eating?! Well, you’re in luck because today we are going to go over how to find the area of a piece of cake, otherwise known as the Area of a Sector!

Now, we’ll all be able to calculate just how much we are overdoing it on that pie! Hopefully, everyone is eating better than I am (I should really calm down on the cupcakes).  Ok, now to our question:

*Also, If you haven’t done so, check out the video that goes over this exact problem, and don’t forget to subscribe! Explanation:

How do I answer this question?

We must apply/adjust the formula for the area of a circle to find the area of the blue shaded region otherwise known as the sector of this circle.

How do we do this?

Before we begin let’s review the formula for the area of a circle. Just a quick reminder of what each piece of the formula represents: Step 1: Now let’s fill in our formula, we know the radius is 5, so let’s fill that in below: Step 2: Ok, great! But wait, this is for a sector; We need only a piece of the circle, not the whole thing.  In other words, we need a fraction of the circle. How can we represent the area of the shaded region as a fraction?

Well, we can use the given central angle value, , and place it over the whole value of the circle, . Then multiply that by the area of the entire circle. This will give us the value we are looking for! Step 3: Multiply and solve! Ready for more? Try solving these next few examples on your own to truly master area of a sector!

Find the area of each shaded region given the central angle and radius for each circle: Check the solutions below, when you’re ready: What do you think of finding the area of sector? Are you going to measure the area of your next slice of pizza?  Do you have any recipes to recommend?  Let me know in the comments and happy calculating! 🙂