Quarter 4 for Dummies 13.5: Law of Sines; SSA

Quarter 4 for Dummies13.5: Law of Sines; SSA By: Megan Wilson & Danial Best

What is SSA? • In any triangle, two sides and an angle that is not included are given to you. • Like this ONE, right here: 25 cm 60⁰ 15 cm

Possible SSA Triangle Cases • You are given D, d, and c • D- angle • d- corresponding side • c- another given side • H=c( • You use this equation when your given angle is acute.

If D is OBTUSE d d c c D D d>c One Triangle d No Triangle

If D is acute d d h c h c d D h<d<c Two Triangles h>d No Triangle D d d h c h c D D d>c One Triangle h=d One Triangle

ExampleSolve ∆ABC w/ A=127⁰ a=63 b=42 = B You would use the Law of Sines = = = .5324 63 Multiply each side by 42. Use the inverse of sine. = 32.2 127⁰ A C 42 And you have your first angle.

ExampleSolve ∆ABC w/ A=127⁰ a=63 b=42 You find your last angle by subtracting the other two from 180 180-32.2-127= 20.8 B 32.2⁰ 63 Now to find the final side. 28 = Use the Law of Sines 127⁰ 20.8⁰ A C 42 USE your Calculator to find what the answer is. c== = 28

Now it’s YOUR turn.  Here’s a blank triangle. Use this one to solve ∆ABC when B=72⁰ b=31 c=28 No peeking at the answers, until you have tried. Answers on next slide.

The… ANSWER Did you get the numbers that are in red, because if you didn’t, you’re WRONG. 72⁰ 28 24.5 Have no fear, the solution is h…….. wait, NEXT SLIDE 48.69⁰ 59.31⁰ 31

Ok, now, the solution is HERE You are given angle B=72⁰, b=31, and c=28. Here’s how you solve it: 72⁰ 28 First, fill in the triangle with what you know so far. 31 Next step = next slide

Next Step = Use the Law of Sines: 72⁰ USE your Calculator to find what the answer is. = = = .86 28 Now, use the inverse of sine and viola, you have angle C. = 59.31 31 Next step = next slide

Next Step Now take 72+59.31 and subtract your answer from 180, to get your last angle. 180-(72+59.31)= 48.69 72⁰ Since, you have all of your angles…. Time to find the last side measurement 28 Use Law of Sines = 48.69⁰ 59.31⁰ 31 Use calculator to solve = = = 24.5

The FINAL Answer 72⁰ 28 24.5 48.69⁰ 59.31⁰ 31

A Word Problem You are trying to get on the roof of your house. Your ladder is 12 feet tall. You place the ladder 7 feet from your house. Find the height of your house where roof and the side of the house meet.

The Solution The answer is 9.7 ft. 35.7⁰ 12 ft. 9.7 ft. 54.3⁰ 7 ft.

Step-by-Step Solution Now the last step. Use Law of Sines again to find the height of the house. = Use calculator to solve. You should have gotten 9.7 ft. First, draw a picture and fill in what you know. Now that you have two angles, go ahead and solve for the last angle: 180-(90+35.7)=54.3 Use Law of Sines to find an angle: = Use calculator to solve. You should have gotten: 0.58 Now take that and plug in into the inverse function of sine, like this: Use calculator to solve. You should have gotten 35.7 B 35.7⁰ 12 ft. 9.7 ft. The answer is 9.7 ft. A 54.3⁰ 7 ft. C

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Quarter 4 for Dummies 13.5: Law of Sines; SSA