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### Missing values in a table. To find the missing values in the table, you need to understand arithmetic and geometric sequences to find the pattern and apply it to the blank space. Watch this for help: https://www.youtube.com/watch?v=fHX3IxwJ61M

Questions 1 - 6

Because these are all right triangles, you can use the Pythagorean theorem to find the missing side. And, because the angles in a triangle always sum up to 180 degrees, you can solve for the missing angle!

Watch this video for a refresher on Pythagorean problems: https://www.youtube.com/watch?v=YlDfGFBNPmA

To find missing angles using the sum of interior angles, check out this video: https://www.youtube.com/watch?v=Dnu-gPjaIdY

Questions 7 - 10

Trigonometric ratios. Use your pre-existing knowledge on the Pythagorean theorem to solve for the missing side lengths. Then, use trigonometric ratios to find the sin/cos/tan of the given angles. Here's a thorough video with an example: https://www.youtube.com/watch?v=Jsiy4TxgIME

Write desired trig ratios and find missing sides of the triangle if any are present.

### Questions 11 - 19

Factor the quadratic equation first. Then, find which inputs make y = 0 to find your x-intercepts, and plug in x = 0 to find the y-intercept. Here's a helpful video with a few factoring examples: https://www.youtube.com/watch?v=YtN9_tCaRQc

Show the factored form of the quadratic and its intercepts.

Question 1

Think about these formulas and feel free to draw helpful diagrams. As you write them, notice the relationship between them, like between the area of a rectangle and a rectangular prism's volume. Here's a refresher video on some volumes: https://www.youtube.com/watch?v=3wuJJqlr6m0

Question 2

You have all the values you would need to solve this, and you wrote the equation you need in the last problem. If you still need help, watch this: https://www.youtube.com/watch?v=O-cawByg2aA

Question 3

You have all the values you would need to solve this, and you wrote the equation you need in the first problem. If you still need help, watch this: https://www.youtube.com/watch?v=9HPWB8UX8GQ

Question 4

You have all the values you would need to solve this, and you wrote the equation you need in the first problem. If you still need help, watch this: https://www.youtube.com/watch?v=2rgSt84wm_Y

Questions 5 - 8

Though it looks like you don't have much, you have all you need. Use the first equation to do an initial sketch of the triangle, find the length of the missing side, and write down the rest of your trig ratios. Here's an example: https://www.youtube.com/watch?v=1mvU2ym9lDY

Question 9

Before getting tripped up in the equation, think about what it symbolizes. Look at your answers above and do some experiments to find the answer. It might also be helpful to write cosine as A/H and sin as O/H and solve to see if you get the same answer.

Question 10

It may help to have an example triangle written out. Think about what the equation is saying: is B equal to 90 - A? If so, then the whole equation could be correct. How will you find out?

Question 11

In this problem, it will be helpful to break each ratio down into its parts (ie. sin = opp/hyp) to see if you can cancel anything out and make tan A * cos A equal to sin A.

Questions 12 - 14

There are many first inputs for rise over run, but they should all lead to the same, simplified answer. Look at this video for an example: https://www.youtube.com/watch?v=2kMUk_XRvRQ

Questions 15 - 17

Use Pythagorean theorem knowledge to find the missing side, then following a rise/run model, find the slope. Remember, check your gut when you get your answer, especially on if it should be positive or negative. (Also remember the formula for slope y-y/x-x) Watch this for some guidance: https://www.youtube.com/watch?v=svbDTxFHHf8

Questions 1 - 3

These problems are telling you essential information about a triangle that exists in real life. Weed out that key information to draw a triangle representing the situation, and use previous knowledge to answer the specific question. Here's a helpful video: https://www.youtube.com/watch?v=svbDTxFHHf8

Questions 4 - 7

Because these are all right triangles, you can use the Pythagorean theorem to find the missing side. And, because the angles in a triangle always sum up to 180 degrees, you can solve for the missing angle!

Watch this video for a refresher on Pythagorean problems: https://www.youtube.com/watch?v=YlDfGFBNPmA

To find missing angles using the sum of interior angles, check out this video: https://www.youtube.com/watch?v=Dnu-gPjaIdY

### Plug the value x = 100 into the explicit expressions you found in questions 11., 12., and 13. and see which value is largest!

Questions 1 - 6

Write and solve a proportion. Think about similar shapes to get in the right mindset. You have all the numbers you need but don't get tripped up on side lengths by forgetting to subtract or add something that should or shouldn't be included in one shape's equation. If you need a refresher, watch this: https://www.youtube.com/watch?v=rgup4S56RYo

Use trigonometric ratio to sketch the right triangle and solve the missing side.

Questions 7 - 12

Because these are all right triangles, you can use the Pythagorean theorem to find the missing side. And, because the angles in a triangle always sum up to 180 degrees, you can solve for the missing angle!

Watch this video for a refresher on Pythagorean problems: https://www.youtube.com/watch?v=YlDfGFBNPmA

To find missing angles using the sum of interior angles, check out this video: https://www.youtube.com/watch?v=Dnu-gPjaIdY

Questions 13 - 18

Use the first equation to do an initial sketch of the triangle, find the length of the missing side, and use the 180 angle sum knowledge or trig ratios to find the missing angle. This video shows a different but similar process that shows helpful steps: https://www.youtube.com/watch?v=1mvU2ym9lDY

Questions 19 - 30

Evaluate trigonometric expressions. These questions challenge you to creatively consider everything you have learned. Think thoroughly about sin, cos, and tan, including how their ratios break down. Some of these questions need you to think about the Pythagorean theorem. Test out your ideas by writing equations and checking your gut.

This video goes through more trig ratios that may provide insight: https://www.youtube.com/watch?v=G-T_6hCdMQc

Question 31

Sketch the situation to find the triangle that you may feel more familiar with. Finding the missing value will build on skills you've practiced in this module. This video covers a similar problem: https://www.youtube.com/watch?v=3H28-wzsF3s

Question 32

Sketch the situation to find the triangle that you may feel more familiar with. Finding the missing value will build on skills you've practiced in this module. This video covers a similar problem: https://www.youtube.com/watch?v=ILQ9TC-0_DA

Question 32

Sketch the situation to find the triangle that you may feel more familiar with. Finding the missing value will build on skills you've practiced in this module. This video covers a similar problem: https://www.youtube.com/watch?v=y0b90Yz-LPM

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