Unit 3 - Day 8

Day 8

Daily Objective: Triangle Inequalities

A triangle inequality is the sum of the measures of any two sides of any triangle is greater than the measure of the third side.

Quiz

1. A triangle has 3 sides but you only know 2. One side is 6 inches long and one side is 8 inches long. What is the range for the third side

2. Billy knows 2 sides of a triangle , one is 9 feet and the other 4 feet. What is the range for the third side.

3. Greg has a triangle that has one side of 7 feet and one side of 8 feet. How long could the third side possibly be?

 

Answer

1. To solve this problem, simply add the 8 and 6 together to get 14 and then minus 6 from 8 to get 2. Then write the equation like this to find your final range. 2 > x > 14.

2. To Answer this problem add the 9 and 4 together and then subtract the 4 from 9 to get a final answer of 5 > x > 13

3. The range for Greg's triangle is 1 > x > 15 because 7+8 is 15 and 8-7 is 1.

Unit 3 - Day 7

Day 7

Daily Objective: Review of Trig

You are now ready for review. Over these next 6 questions you will review everything we have learned these last 6 days.

Review

1. Trey is building a roof truss and wants to find the angle of it if it's 2 feet tall and 3 feet long on the bottom.

2. If a right triangle has an angle of 27 degrees and an adjacent angle of 12 feet, how long is the hypotenuse?

3. A small right triangle has a bottom side of 3 feet and a hypotenuse of 5 feet. a large triangle has a bottom of 7 feet but no one knows how long the hypotenuse is. Find the length of the hypotenuse.

4. Mark has decided to find the slope of a right triangle that has an adjacent side of 7 feet and a opposite side of 3 feet. He thinks the slope is 24. Is he correct?

5. A triangle has a bottom length of 19 inches, the bottom right angle is 83 degrees and the bottom left angle is 72 degrees. What is the length of the left side of the triangle.

Answers

1. To solve this problem simply divide 2 by 3 and then use the tangent-1 function to get a final answer of 33.7.

2. For this problem all you have to do is divide 12 by 27cosine and that will leave you with a final answer of 13.47 feet. 

3. You have to set up the problem like 3/5 x 7/x. Then you cross multiply them to get 35/3x. Then divide the whole thing by 3 to get a final answer of 11.67 feet.

4. The correct answer is no he is not correct because if you divide 3 by 7 and then take that by tangent-1 you get 23.2 as your slope.
5. For this problem first you must find the third angle, which is 25 degrees. Then you have to set up the problem like this: sine25/19 x sin72/x. You must then cross multiply the 19 and sine72 and then divide by sine25 to get your final answer of 42.76.

Unit 3 - Day 6

Day 6

Daily Objective:

Non Right Angle Triangle Trig: Law of Sines, Area of a Triangle.

The Law of Sines is a mathematical formula used to find the angles and side lengths of triangles that don't have a right angle in them. However you still need 1 side length and all three angles. You can use this formula to find the sides of any triangle as long as you know the angles.

Figure 1

Quiz

1. We'll be using Figure 1 for all three questions today. For this first problem the top angle is 50 degrees, the left one is 70 degrees, and the right one is 60 degrees. The bottom of the triangle is 20 feet. How long is the left side?

2. Now the triangle is slightly different. The left corner is 30 degrees, the right corner is 57 and the top angle is 93 degrees. The right side is 4 feet and the left side 5 feet. How long is the bottom? 

3. A triangle has a bottom of 10 feet. The left angle is 48 degrees and the right angle is 12 degrees. How long is the left side.

Answers

1. To solve this problem you need to set it up like this: sine50/20 x sine60/x. Then you must cross multiply the 20 and the sine60. After you have done this you then divide by sine50 to get a final answer of 22.61 feet.

2. You can set up this problem 2 ways but I am going to do it with the right side. Set up the problem like sine30/4 x sine93/x. Cross multiply the 4 and sine93 and then divide by sine30 to get a final answer of 7.9 feet.

3. First find the last angle which is 120 degrees. Then set up the problem like sine120/10 x sine12/x. Then cross multiply the 10 and sine12 and then divide by sine120 to get a final answer of 2.4 feet.

Unit 3 - Day 5

Day 5

Daily Objective:

Tangent and its relationship to slope.

Tangent

The tangent function is the slope of a triangle. Think about it, if you make a triangle on a graph out of your line of best fit, then to find the slope you would have to use the opposite and adjacent sides. The tangent function uses those sides and therefore finds the slope.

Quiz

1. If someone saw a 14 foot long roof and it was 6 feet tall, what is the slope of the roof? (Hint the whole roof is 14 feet long.)

2. Max drew a blue card that tells him to help make roof trusses. The roof trusses for this house need to be 24 and a half feet across and 4 feet tall. What is the slope of the trusses for this house?

3.Doug want to do a little DIY on his house and decides to make a little toolshed in his back yard. He bought 10 foot boards for the adjacent side of the trusses for the shed of his roof and 3 foot boards for the opposite sides of his roof. What will the slope of his shed be?

Answers

1. The first thing you must do for this problem is divide the 14 by 2, because that is the whole length of the roof and we only need half. Then you take take the 6 and divide it by the 7 that you just found and that will leave you with .857......and so forth. You then take that and push the tan-1 function and that will leave you with a final answer of a slope of 40.6. 

2. This problem is easier in the fact that all you need to do is divide 4 by 24.5. That will leave you with .163......something which you take by the tan-1 and that will leave you with a final slope of 9.27.

3. This problem is set up like the others in which you must divide the opposite over the adjacent, 3 divided by 10, which is .3. Take that by tan-1 and that leaves you with a final slope of 16.7.

Unit 3 - Day 4

Day 4

Daily Objective: Linear Inequality Review

Sine

Cosine

Tangent

Lets take a small review over what we have learned so far. First, we learned about inverse sine, inverse cosine, and inverse tangent. These functions are used to find angles in a right triangle. Then we learned about regular sine, cosine, and tangent. These math functions are used to find side lengths on a right triangle. Then lastly we learned about how to use these two ideas together.

Review

1. Billy is making a truss for his geometry and construction class. The adjacent side is 17 feet long and the hypotenuse is 20 feet long. Find the angle using the cosine function.

2. Find the slope of the stairs in if the rise of the stairs is 4 inches and the run of the stairs is 8 inches.

3. Billy is a student and he is building a  wooden right triangle for a project. The hypotenuse needs to be 2 feet long and the height needs to be 6 inches tall, what  is the angle of his triangle.

4. There are 2 sizes of roof trusses that need to be built for geometry and construction, and they are similar triangles. The bottom side of the smaller triangle is 12 feet and the right side is 9 feet. The bottom side on the big triangle is 20 feet but no one knows how long the right side is. How long is the right side?

5. If the hypotenuse of a large right triangle is 12 inches and the bottom is 7 inches. A smaller right triangle, which is similar to the first, has a hypotenuse of 7, but what is the length of the bottom side.

6. A tree is 14 feet tall and has a 20 foot shadow. A smaller tree is 9 feet tall. How long is the smaller tree's shadow.

Answers 

1. For the first problem you need to divide the adjacent side by the hypotenuse so the would be 17/20. That equals .85. Then you take .85 and then use the cosine-1 function. That will tell you that the angle of the truss is 58.21 degrees.

2. For problem #2 you'll need to use the tangent function. The first thing you do is divide the opposite side by the adjacent side. That would be 4/8 which would leave you with .5. Then use the tan-1 button and that leaves you with a final answer of 26.57 degrees for your angle.

3. The first thing you must do for this problem is convert the 2 feet into 24 inches. Then you must divide the 6 by the 24 and then push the sine-1 button and that will leave you with an answer of 14.48 degrees.

4. To solve this problem, first you must set up the equation 9/12 x x/20. Then you have to cross multiply the 9 and 20 and the x and 12. This will leave you with 12x/180. Take that number and divide both sides by 12 and that will leave you with final answer of 15 feet.

5. This problem is set up just like problem number 5, except with the numbers 12/7 x 7/x. Cross multiply those numbers and that will leave you with 84/7x. Divide that number by 7 and that will leave you with final answer of 12 inches.

6. This problem is set up just like the last to with the numbers 14/20 x 9/x. Cross multiply and divide by 14 and your final answer is 12.85 feet.

(Yes I did type up all of these answers.)

Unit 3 - Day 3

Day 3

Daily Objective:

Sine, Cosine, Tangent and their inverse continued Sin/Cos of complementary angles.

Figure 7

Quiz

1. Using Figure 7 determine angle x.

2. Using Figure 8 determine angle x.

3. Using Figure 9 determine angle x.

Figure 8

Figure 9

Answers

1. Firstly, set up the problem 7/8 x x/6 and cross multiply. That will give you 8x/56 and then divide that number by 8 and that will give you the hypotenuse for the smaller triangle. You'll then want to divide the 6 by the 7 and then use the
sine-1 function which will give you a final answer of 59 degrees.

2. You have to set this problem up the same way as the first one. 3/4 x x/8 and cross multiply to get 4x/24 and divide by 4. Take the 6 that you just got and divide that by 8, leaving you with .75, which you will then use the tangent-1 function on to get a final answer of 36.87 degrees.
3. You first set up the problem like x/5 x 9/4 and cross multiply to get 40/4x. Divide that by 4 and you'll get 10. Divide the 5 by the 10 to get .5 and then use the sine-1 function to find the final angle of 30 degrees.

Unit 3 - Day 2

Day 2

Daily Objective:

Sine, Cosine, and Tangent functions using similar triangles.

These functions are used to find the sides of a triangle. However today we are going to use them with similar triangles. a similar triangle is a triangle that is the same shape but is not the same size. You can use these triangles to find sides on another triangle if you know two sides on one triangle and one side on the other.

(Angle A is equal to angle E, angle B is equal to angle G, and angle C is equal to angle F.)

Figure 4

Quiz

1. See Figure 4.

2. Using Figure 5 determine the length of side x.

Figure 5

3. Using Figure 6 determine the length of side x.

Answers 

Figure 6

1. First you must set up the equation like 5/5 x x/10. You then have to cross multiply the 5 and 10 and the 5 and x. This will leave you with 5x/50. you then divide the entire problem by 5

2. First you set up the problem like this- 6/10 x 12/x. You then  cross multiply the 10 and 12 and the x and 6. This will leave you with 120/6x. You then divide both numbers by 6 and that leaves you with an answer of 20.

3. Set up the problem like 4/8 x 7/x. Then cross multiply the 8 and 7 and the 4 and x and you'll end up with 56/4x. Then divide that entire problem by 4 and you'll end up with a final answer of 14.