8.1 notes right triangle...

8.1 Notes Right Triangle Review.notebook January 22, 2016


Simplifying Radicals Activity:

Now you try a couple!


Check your work:

1. 2.

3. 4.


Not all radicals can be simplified further. Why not?


Rationalizing the DenominatorActivity:Two examples:

Now you try a couple!


Check your work:

1. 2. 3.


A Quick Review of

Right Triangle TrigonometryUnit 8 Day 1

Hypotenuse is always across from the right angle

Note: is the greek letter "theta" and is often used to represent angles.


There are three main trig functions:

• Sine, defined as the ratio of the opposite leg to the hypotenuse

• Cosine, defined as the ratio of the adjacent leg to the hypotenuse

• Tangent, defined as the ratio of the opposite leg to the adjacent leg

opphyp

oppadj

hypadj

3

4 5o h

a

click here for an example


Graphing calculators default to a mode called radian mode (more about radians later...yay!). Today, we will be dealing with degrees, so we need to be in degree mode.

Before we move on...

Hit the mode button & Change to DEGREE


Use a trigonometric function to find the value of x.

Find a Missing Side LengthExample 1:


Find the value of x.

Find a Missing Side LengthPractice A:


A Brief Aside on Inverse Trig Functions...When solving an equation for x, you have to "undo" whatever is being done to x.

So, what if our variable is an angle?

We need to "undo" whatever is being done to x. In this case, sine. To undo sine, use inverse sine (sin1).

sin1 sin1

Practice a couple:


Find a Missing AngleExample 2:Find the measure of .


Find a Missing AnglePractice B:

Find the value of x.


If , find the exact values of the two remaining trig ratios for B.

Find ALL Trigonometric RatiosExample 3:


Find Trigonometric RatiosPractice C:


Real World Example:To calculate the height of a building, Joel walked 200 feet from the base of the building and used an inclinometer to measure the angle from his eye to the top of the building. If his eye level is at 6 feet, how tall is the building?

Pull


Real World Example:Two bicycle ramps each cover a horizontal distance of 8 feet. One ramp has a 20o angle of elevation, and the other ramp has a 35o angle of elevation, as shown at the right.

b. How much taller is the second ramp than the first? (Round to nearest tenth.)

c. How much longer is the longer ramp? (Round to nearest tenth.)

a. Without calculating, which ramp is longer?


Challenge Time:A line segment has endpoints A (2,0) and B (6,5). What is the measure of the

acute angle formed by the line segment and the xaxis? Explain how you

found the measure.

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8.1 notes right triangle...

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