Unit 5 trigonometric functions homework 5 solving right triangles

Homework for Tuesday, November 13th: p. 45- 46 (questions 1-10) AND P. 52 (questions 5-11)

Homework for Wednesday, November 14th: p. 58-60 (questions 1-10)

Solutions for Day 2 Homework

P. 64 - 65 Questions 7-30 (I originally assigned p. 66 - It is an EXTENSION. You do NOT need to do it for homework because it is much harder than anything you would see on the test (or in real-life).

Homework key for 11/15/18

Stuff to know for your test.

• Ratios for sine, cosine, and tangent. SOH-CAH-TOA
• Know how to find an angle measure when given two sides (sine inverse, cosine inverse, tangent inverse).
• Be able to solve word problems like we did in class. I've posted a key below. I've also posted additional word problems and the key below if you want more practice.
• Be able to prove if a trigonometry statement is true or not. (Ex. is sin(A)=cos(B)?). Be able to use some of these statements. Go back and look at the Conjecture section of our packet if you don't remember.

Key for Packet from Class

Additional Practice Word Problems (not required unless you want more practice)

Packet for Right Triangle Trigonometry

MCR3UUnit5TrigRatios

1

5.1 Trigonometric Ratios in Right Triangles

3 Primary Trig Ratios:

Reciprocal Trig Ratios

Remember :

SOH CAH TOA

•To solve a triangle means to determine

all unknown side lengths and angles

A

B

C

3

4

Write the 6 trig ratios for angle A

Solve for angle A

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This Unit will cover the following topics:​

• Pythagorean Theorem
• Special Right Triangles
• SOH CAH TOA: Finding Missing Angles and Sides​

Pythagorean Theorem

Special Right Triangles

There are 2 special right triangles we need to know: 30-60-90 and 45-45-90

SOH CAH TOA

SOH CAH TOA is an acronym used to find missing sides and angles of right triangles (its not just a jumble of letters!)

Finding Missing Angles:  When given 2 sides of a right triangle, we can find a missing angle. SOH CAH TOA tells us which function to use based on which sides were given (the side adjacent to the missing angle, opposite or hypotenuse). SOH CAH TOA gives us the ratio of the missing angle and the inverse function on our calculator turns that function into an angle measurement. Remember to make sure your mode is set to degrees not radians

Finding Missing Sides: If we know an angle and a side, we can find the other missing side by going in reverse. Figure out which function to use based on the side that you have and the side that you need to find in relation to the given angle. Then take the COS, SIN or TAN of that given angle (not the inverse! inverse takes ratios and turns them to angles. We need to take an angle and make it a ratio) and set it equal to the ratio of the known side and unknown side and solve for x.

Below is the powerpoint that we used in class to introduce SOH CAH TOA and the missing angles

Now lets take what we know about the ratios and apply them to find missing sides and angles

Word problems take what you know about solving for missing angles and sides and turn it into real world application. To solve a lot of the SOH CAH TOA word problems, you need to understand Angles of elevation and depression.  Below are 2 videos that re-explains what it is and goes through practice problem with you. 

Anticipated Day of Testing: Thursday, December 6

Please note the answer to the review #5 on the review below is incorrect. The angle of depression is not properly labeled. You should use Cos 57, as thats 90 degrees minus the angle of depression.