Journal chapter 7-8

1. Journal chapter 7-8 Jose Antonio Pomes 10-5

2. Describe a ratio. Describe a proportion. How are they related? Describe how to solve a proportion. Describe how to check if a proportion is equal. • - A ratio is when two numbers are compared by division. • - A proportion is when you say that two ratios are equal. • They are related because when you state a proportion you are using rations so they basically need each other. • To solve a proportion first you need to cross multiply. Then if you have a third value then you divide by it and this would give you the answer. Another way is that after you cross multiply you set them equal to each other and its a algebraic equation.

3. 3 examples are rise run rise run rise run

4. Describe what it means for two polygons to be similar. What is a scale factor? Give at least • If two polygons are similar then they have the same shape but are different size. For two polygons to be similar their corresponding angles have to be congruent and their corresponding sides need to be proportional. • A scale factor is the ration of any two corresponding lengths in any two two figures. This can describe how much the figure expanded or reduced.

6. Describe how to find the scale factor for the perimeter and areas of similar figures. • The scale factor of the perimeter is equal to the ration of similarity. • The scale factor of the area is equal to the second ratio of similarity.

7. p = 12 p = 14 a = 10 a = 9 p = 14 a = 12

8. Describe how to use similar triangles to make an indirect measurement. - Indirect measurement is when you use any method to use formulas, similar figures or proportions to measure any object. You use the sides of the similar triangles to use indirect measurement.

10. Describe the right triangle altitude proportionality theorem. Explain how the proportions can be used to solve real life problems. - When you draw the altitude to the hypotenuse in a right triangle they you are forming 2 new triangles. All of these 3 triangles that you have are now similar figures. - Proportions can be used in real life problems like if you are climbing a cliff, you know how long is the shadow, your height and your shadow but you want to know the height of the cliff. You can use proportions from you to the cliff to find out.

12. Describe the three trigonometric ratios. Explain how they can be used to solve a right triangle. What does it mean to solve a triangle? How are they used in real life? • The three trigonometric ratios are Sine, Cosine and Tangent. You can use sine if you have an angle, its opposite side and its hypotenuse. You can use cosine if you have an angle, its adjacent side and its hypotenuse. You can use tangent if you have an angle, its opposite side and its adjacent side. You use this ratios to find our the length of sides. • If you are trying to find an angle they you can use the inverse of this ratios based on the information that you have. To solve a triangle means to find our all the angles and all the sides. They can be used to figure out distances.

13. sin 40 = 15/20 tan 90 = 20/10 cos 50 = 15/20 50 20 15 90 40 10

14. Compare an angle of elevation with an angle of depression. How are each used? - The angle of depression is the angle formed by a horizontal line and a line of sight to a point below that line. - The angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line.

15. Angle of depression Angle of Elevation