# Finding Trigonometric Ratios04:29 minutes

Video Transcript

## TranscriptFinding 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