# Finding Trigonometric Ratios 04:29 minutes

**Video Transcript**

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Transcript
**Finding Trigonometric Ratios**

Let me tell you a *tail* of the Pharaoh SOH-CAH-TOA. To honor Pharaoh SOH-CAH-TOA, a huge *PURR*-amid...pyramid was constructed.
The pharaoh, who is *paw*-sitively crazy for cats, ordered a pyramid from the pyramid-building company, Cleo-CAT-ra, for his cat to live in since pyramids are the *PURR*-fect shape. To **determine** the **dimensions** of the miniature pyramid, we *gato* use **trigonometric ratios**.

### Three Trig Ratios

Let’s review the **ratios** to help the Pharoah so we can help him avoid a *cat*-astrophy. For **right triangles**, the most common **trig ratios** are **sine**, **cosine** and **tangent**. Let’s take a look at the three ratios. You should remember that the **sine** of ∠A is the **length** of the **opposite side divided** by the **length** of the **hypotenuse**. The **cosine** of ∠A is the **length** of the **adjacent side divided** by the **length** of the **hypotenuse**. And finally, the **tangent** of ∠A is the **length** of the **opposite side divided** by the **length** of the **adjacent side**.

You won’t believe this, but the pharaoh’s name is a mnemonic device we can use to remember these **three trig ratios**! Let's *paws* and have a look: SOH, CAH, TOA. It’s easy to get confused about which side is which. The **hypotenuse** is always **located opposite** the **right angle**. The other two sides are named depending on the angle in question. The **opposite side** is **across** from the **target angle** and the **adjacent side** is **between** the **target angle** and the **right angle**.

### Calculating Trig Ratios

The Pharoah is not *kitten* around. Since he already knows the trig ratios, he can figure out the trig ratios for his pyramid by using the measurements he knows. Look at the triangle face of the pyramid. Dividing a side of the **base** by 2 and drawing in an **altitude** gives us two **right triangles**. Since each side of the base is 755 ft we can divide the base by 2, to calculate the length of the side adjacent to ∠A. Now we know all three lengths: The length **adjacent** to ∠A is 377.5 feet. The length of the **hypotenuse** is 610 feet, and the length **opposite** ∠A is 479.16 feet. Let's **calculate** the **trig ratios**!

To calculate the **sine** of an angle, simply **divide** the length of the **opposite** side, 479.16, by the length of the **hypotenuse**, 610. To get the **cosine**, **divide** the length of the **adjacent** side, 377.5, by the length of the **hypotenuse**, 610. And last, but not least, **divide** the length of the **opposite** side, 479.16, by the length of the **adjacent** side, 377.5, to get the **tangent**.

### Calculating the side lengths with given trig ratios

Now the pharaoh can use this information to **calculate** the **measurements** for the **miniature** pyramid. Because the kitty cats' pyramid will be a similar version of the pharaoh's, the trig ratios will be the same. If the miniature will have a height of 20 feet, what are the other lengths? Chose the **trig ratio** that will help you to **calculate** the **unknown length** with the fewest steps.

Let's use the tangent ratio, which is 1.269, to set up a proportion using 20 as our opposite side length. Now we have to ***solve** for the adjacent side. Using **opposite operations** and **isolating** our **variable**, we find that the adjacent side is equal to 15.76 feet. This is just half the **base** of the face of the pyramid, so we **multiply** by 2 to **determine** the full length of the base. Pharoah SOH-CAH-TOA's looks at the plans he's *feline* pretty good about the mini pyramid right about now!

The Pharoah is speechless! I guess the cat's got his tongue! Ugh...All these cat puns are freakin' *meowt*

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2 commentslol

That cat pun counter really worried me with the amount of numbers available!