TISK problems Solve each equation. Monday, August 22, 2011

Homework Discussion H  Proper Heading: Complete, right location, all parts in proper places  This part of your grade is just for ME, everything else is meant to help YOU. P  Problems are copied down. There is enough information so that anyone looking at the paper can tell what the question was asking. W  Work is shown. You defend your answer in some way. A  Answers are indicated. It is clear and easy to see your answers because they are either boxed, circled, or highlighted. C  Complete all problems. If you are confused by a problem, you’ve listed everything you could figure out about it, shown any work we did together in class (in another color) if we did review that problem, and asked a meaningful question if still confused.

Trigonometric Ratios A young Indian, frustrated by his inability to understand the geometric constructions of his tribe's battle dress, kicked out in anger against a stone and crushed his big toe. ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Fortunately, he learned from this experience, and began to use study and concentration to solve his problems rather than violence and injure himself. This was especially effective in his study of math, and he went on to become the wisest man of his tribe. He studied many aspects of trigonometry; and even today we remember many of the functions by his name.

When he became an adult, the tribal priest gave him a name that reflected his special nature -- one that reminded them of his great discoveries and of the event which changed his life. Because he was troubled throughout his life by the problematic toe that he injured by kicking the stone, he was constantly at the edge of the river, soaking his toe in the cooling waters.

SohCahToa For that behavior, he was named Chief Soh Cah Toa.

What significance is this story to us? Soh Cah Toa SOH  SOH: Sine of an angle = Opposite over Hypotenuse CAH  CAH: Cosine of an angle = Adjacent over Hypotenuse TOA  TOA: Tangent of an angle = Opposite over Adjacent

Uhhhhh… okay, so what does that mean? First let’s clear up some terms.  Opposite Whichever side is across from the angle a is opposite b is opposite  Adjacent Whichever side is next to the angle, and is not the hypotenuse a is adjacent to b is adjacent to  Hypotenuse The side across from the right angle A B C a b c

SOH-CAH-TOA So what does SOH CAH TOA mean? First, some abbreviations: sine = sin cosine = cos tangent = tan A BC a b c

Example 1. Find the sin, cos, & tan for angle A B A C 13 Some of the most common Pythagorean Triples are: 3, 4, 5 5, 12, 13 7, 24, 25 8, 15, 17 9, 40, 41 11, 60, 61

Check Point. Find the sin, cos, & tan for each indicated angle a)b) A B

Take a look at special right triangles… Find the sin, cos, & tan for a 45º angle º

Take a look at special right triangles… Find the sin, cos, & tan for a 30º and a 60º angle º 60º

Using Trig to Find Measures You’re standing 30 feet away from the wall of a building. The angle of elevation from where you’re standing, to the top of the wall is 72º. How tall is the wall? 30 ft you Not drawn to scale 30 ft is adjacent to the 72º angle. The height of the building is opposite the angle. We will find the tangent of 72º. Approximately 92.3 ft tall.

Check Point. Find the height of the tower. 154 ft you

Error Analysis To find the measure of, Abby sets up the following equation: What mistake is she making? How can she find the measure of ? A B C 15

A B C D

Solving Right Triangles Solving a right triangle means…  … you are given two side lengths…  … or one side length and one acute angle measure…  …and you want to find all the other angles and/or sides!

Using Calculators to Help Us Out! tanA = 0.7  Find the measure of angle A. Type tan -1 (0.7) into your calculator and hit enter. This operation asks “For what angle measure does the tangent equal 0.7?” Answer? sinA = 0.9  Find the measure of angle A.  Type sin -1 (0.9) into your calculator and hit enter.  This operation asks “For what angle measure does the sine equal 0.9?”  Answer? cosA = 0.1  Find the measure of angle A.  Type cos -1 (0.1) into your calculator and hit enter.  This operation asks “For what angle measure does the cosine equal 0.1?”  Answer?

Using Calculators to Help Us Out! tanA = 0.7  Find the measure of angle A. Type tan -1 (0.7) into your calculator and hit enter. This operation asks “For what angle measure does the tangent equal 0.7?” Answer? sinA = 0.9  Find the measure of angle A.  Type sin -1 (0.9) into your calculator and hit enter.  This operation asks “For what angle measure does the sine equal 0.9?”  Answer? cosA = 0.1  Find the measure of angle A.  Type cos -1 (0.1) into your calculator and hit enter.  This operation asks “For what angle measure does the cosine equal 0.1?”  Answer? Remember, 0.7, 0.9 and 0.1 are just fractions! You could enter them this way into your calculator. Try it: tan -1 (7/10) sin -1 (9/10) cos -1 (1/10)

Solve the right triangle. Round decimals to the nearest tenth. 28 ⁰ 8 B A C Step 1: Do you have enough information? Needed:  1 side  1 angle or 1 other side Step 2: Determine what else you’re looking for. Needed:   AB  AC Step 3: Solve for anything “easy” like 1 missing angle or 1 missing side. Step 4: Set up trig-ratios to solve for the rest. adj opp hyp

How do you solve a right triangle? Solve the right triangle. Round decimals to the nearest tenth. 7 9 B A C Step 1: Do you have enough information? Needed:  1 side  1 angle or 1 other side Step 2: Determine what else you’re looking for. Needed:    AC Step 3: Solve for anything “easy” like 1 missing angle or 1 missing side. Step 4: Set up trig-ratios to solve for the rest. adj opp hyp adj opp

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