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.)