Day 2: Students will define sine, cosine, and tangent functions using similar triangles. For sine, you use the angle of a corner of the triangle, the opposite side of a triangle, and the hypotenuse of the triangle. For cosine, you use the angle of a corner of the triangle, the adjacent side of the triangle, and the hypotenuse of the triangle. For tangent, you use the angle of a corner of the triangle, the adjacent side of the triangle, and the opposite side of the triangle.

Quiz:

1. What is the length of the hypotenuse of a right triangle if the angle is 50 degrees and the opposite side is 10?

2. What is the length of the adjacent side of a triangle if the angle is 60 degrees and the hypotenuse is 10?

3. What is the length of the opposite side of a triangle if the angle is 40 degrees and the adjacent side is 5?

Answer Key:

1.

The length of the hypotenuse is 13.05 units.

2. 

The length of the adjacent side is 5 units.

3. 

The length of the opposite side is 4.19 units.

Tips from the pros video:

To view our video click the link below:


http://www.youtube.com/watch?v=w7_l8znL5NE

Day 8: Students will define triangle inequalities. Triangle inequalities is finding the range for the third side of the triangle when two of the lengths of the sides are already given.

Quiz:

1: If one side of a triangle is 6 and the other side is 8, then what is the range that of numbers that the third side can be? Write it as an equation.

2. If one side of a triangle is 10 and the other side is 4, then what is the range that of numbers that the third side can be? Write it as an equation.

3. If one side of a triangle is 5 and the other side is 12, then what is the range that of numbers that the third side can be? Write it as an equation.


Anser Key:
1.

 

The range is 2-14 and the equation is 2<_x<_14.

                                                               

2.

 

The range is 6-14 and the equation is 6<_x<_14.

3.

 

The range is 7-17 and the equation is 7<_x<_17.

 

 

Day 7: Students will review the trig functions; sine, cosine, and tangent. Students will take these trig functions and use them in real world problems. When using tangent, you either need to know an angle in a triangle, the adjacent side, or the opposite side. When using tangent, you are trying to find one of the three things I mentioned earlier. When using cosine, you either need to know an angle in the triangle, the adjacent side, or the hypotenuse. When using cosine, you are trying to find one of the three things I just mentioned. Lastly, when you use sine, you either need to know an angle in the triangle, the opposite side, or the hypotenuse. When using sine, you are trying to find one of the three things I just mentioned.

Quiz:

1. If a ramp is 5 feet tall and the angle of the ramp from the start to the top is 50 degrees, how long is the actual sloping part of the ramp?
2. If you are standing 10 feet away from the tree and the angle from you to the top of the tree is 60 degrees, how tall is the tree?
3. If If you are standing by a building, the distance from you to the top of the building is 1,000 feet, and the angle from you to the top of the building is 70 degrees, how far away are you from the building?

Answer Key:

1.

The sloping part of the ramp, or the hypotenuse, is 6.52 feet long.

2. 

The tree is 17.32 feet tall.

3.

You are 342.02 feet away from the building.

Day 6: Students will define law of sines and the area of triangles. To use the law of sines in order to find the length of one of the sides on a triangle, you take the angle of one of the corners in the triangle and you put that number over the length of the side directly across from, or opposite of, that angle. Next, You use the angle that is opposite of the side you need to find, and you put the angle over x. The last step is you set these two fractions equal to each other and solve from there. To find the area of a triangle, you do base times height divided by two.

Quiz:

1. If in a triangle side B is 7 inches, angle B is 35 degrees, and angle C is 105 degrees, how long is side C?
2. If in a triangle side A is 10 inches, angle A is 50 degrees, and angle B is 100 degrees, how long is side B?
3. If a triangle has a base of 10 feet and the height of the triangle is 5 feet, what is the area of the triangle?

Answer Key:

1.

Side C is 11.78 feet long.

2. 

Side B is 12.8 feet long.

3. 

The area of the triangle is 25 feet square.

Day 5: Students will define tangent and it relationship to slope. Tangent is the trig function you use to find either the opposite or adjacent side of a triangle when you are given either the opposite or adjacent side and an angle within the triangle. So, for example, you would use tangent if you knew what the length of the opposite side and an angle in the triangle were but needed to find the length of the adjacent side. Tangent relates to slope because to find slope you need to know rise and the run of a triangle, and to use tangent you need to know either the opposite or adjacent side of a triangle and you are trying to find either the opposite or adjacent side of a triangle; the rise and the run of a triangle are the adjacent and opposite sides.

Quiz:

1. What two sides of a triangle are associated with tangent?
2. If the opposite side of a triangle is 4 and the adjacent side of the triangle is 1, what is the slope of the triangle?
3. If you you know that the opposite side of a triangle is 2 and the angle of the triangle is 50 degrees, what is the length of the adjacent side?

Answer Key:

1.

The two sides are the adjacent side and the opposite side.

2.

The slope is 4/1.

3.

The length of the adjacent side is 1.67 units.

Day 4: Students will review linear inequalities. Linear inequalities are when you have an equation that you need to solve and then graph. Then, you shade either below or above the line.

Quiz:

1. Graph the following equation: y>2x+1.
2. Graph the following equation: y<2x+1.
3. Graph the following equation: y<3x-2.


Answer Key:

1.

You start at 1 and everytime you go up 2 over 1 and place a dot. Shade above the line because y is greater than 2x+1.
2.

You start at 1 and everytime you go up 2 over 1 and place a dot. You shade under the line because y is less than 2x+1.

3.

You start at -2 and everytime you go up 3 over 1. You shade under the line because y is less than 3x-2.