Journal Chapters

7 & 8

By: Ana Cristina Andrade

Ratios and proportions:

The relation between a ratio and a proportion is: the proportion shows that two ratios are equal.

If 84 is divided into three parts in the ratio 3:5:6, what is the sum of the smallest and the longest part?

Ratios: a comparison between two valuesSlope: rise/run = y2 – y1/ x2-x1

Proportion: equation stating that two ratios are equal.

Given that 29=8b, find the ratio of A to B in simplest form

An architect´s model for a building is 1.4m long and 0.8m wide. The actual building is 240m wide. What is the length of the building?

Solving proportions:To solve proportions you use cross products (cross multiplying) and solve by using algebra.

Checking if proportions are equal:

To check substitute the answer in the variable and compare the two ratios. If they are equal it is correct.

Similar polygons:Similar polygons: corresponding angles are congruent & corresponding side lengths are proportional.

Scale factor: the ratio of corresponding measures, describes how much the figure is in large or reduce

Indirect measurement:To find indirect measurement in a similar triangle, there are two ways to do it. For example, if you want to measure a tree, you set a mirror on the

ground and move away from it until you can see the point of the tree. When you´ve done it, you measure the distance between you and the mirror , the distance between the mirror and the three, and your height. You plug the distances in a proportion and you solve.

The second way to measure a tree is using its shadow. You measure the distance from the tree to the shadow, the distance from the person to the shadow, and the height of the person. You plug them in in a proportion and you solve.

Why is this an important skill?With the example of the tree, if I would like to cut a tree down, first I

would see if the tree would hit my house or any other important object around it. To do it, it would be difficult to measure it the normal way. There is when I would use the indirect measurement.

To find the height of a tree, a student measured the tree´s shadow and her own shadow. If the student´s height is 5 ft, what is the height of the tree?

A student who is 5.1 ft tall measured her shadow and the shadow cast by a water tower shaped like a gold all. What is the height of the tower?

To find the height of a building Amir placed a mirror on the ground 40ft from its base. Then he stepped back 4ft so that he could see the top of the building in the mirror. Amir´s ayes were approximately 5ft,6 in above the ground. What it the heigh of the building?

scale factor to find the perimeter and area of a new similar figure:

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To find the area using scale factor you simplify the fraction of the two shapes (smaller shape/bigger shape) and then you square the fraction.

To find the perimeter using scale factor you find the perimeter of each triangle, then create a fraction with each perimeter (smaller shape/ bigger shape). Then you simplify the fraction. The ratio of the perimeter is the same as the ratio of their sides.

The ratio of the perimeter of the blue rectangle to the perimeter of the green rectangle is 4:7. Find X

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X

What it the scale factor of the perimeter of the rectangles?7

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Trigonometric ratios:•SinA: Opposite/hypothenuse•CosA:adjacent/hypothenuse•TanA: opposite/adjacent

Hypotenuse

Adjacent

OPPOSITE

Solving a triangle: find all of the angles and all of the sides measures.

Finding trigonometric ratios in special right triangles: Decide which angles you would like to solve for and you choose and solve between the three trigonometric ratios.

Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundreth.

Find the length PQ in the triangle

Solve the triangle

Angle of elevations Vs.Angle of depression:

Angle of depression

Angle of elevation

The angle of elevation is the angle formed by a horizontal line joined with a line that has a point above the line while the angle of depression is a horizontal line joined with a line that has a point below the line.

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Classify each angle as angle of depression or angle of elevation

1. <1 – elevation2. <2 – depression3. <3 – elevation4. <4 - depression

When the angle of elevation to the sun is 37°, a flagpole casts a shadow that is 24,2 ft long. What is the height of the flagpole to the nearest foot?