5.13 Solving Triangles with Trigonometry #(1,2,4,8,11,15)

I. Right Triangles SOH CAH TOA helps you remember which trig function to use in order to find sides or angles of a right triangle. When you Input angles into the primary trig functions, the output is the ratio of the sides of a right triangle When you Input ratios of a right triangle into the inverse trig functions the output is the angle.

Solving Right Triangles SOLVE TRIANGLE ABC A x Means to find the measure of all the missing angles and the length of all the missing sides 5 C B 2 To Find Angle A: To Find Angle C: Use Tangent to find Side AB:

II. Non Right Triangles Law of Sine Law of Cosine Applications

Introduction to Law of Cosine Formula: The small letters stand for the sides (a,b,c), While the capital letter stands for the angle (A) Use law of cosine when you are not given a right triangle, and you have two sides, and one angle that is in between the two sides

Law of Cosine Formula for Law of Cosine FIND SIDE BC C 10 a (<A = 44 Degrees) A Stick the numbers in… 8 B

Introduction to Law of Sine Formula: Like law of cosine, the lower case letters represent the sides, while capital letters represent the angles Use law of Sine when you have an angle and a side that are opposite to each other.

Law of Sine Find side a Formula for Law of Sine : (<A = 40 Degrees) Given (<A = 40 Degrees) (<C = 80 Degrees) Formula for Law of Sine : 10 A B Put the numbers in… C  

Tips & Proven Strategies Use law of sine when you have pairs. Use law of cosine when you have no pairs. Remember to draw diagrams to help you. When several steps are involved, don’t round the numbers. Keep the original, and round at the very end. By doing this, your answer will be more accurate.

Problem Solving With Trig The Rays are under new coaching, they’ve been told that a sure to win technique is to block goals in precise triangles. If Bertuzzi and Cloutier are 4 feet away from each other, and Cloutier and Sopel are 6 feet away, how far is Sopel from Bertuzzi, if Cloutier is 36 degrees away from them both? Remember to first draw a diagram, and label the sides with information you know. Now since you know 2 sides and one angle, you can use Cosine Law: B c? 4 S 36 C 6

Short Quiz 1. Determine the length of QR to the nearest millimeter. 2. Calculate Angle R to the nearest tenth of a degree. 3.Calculate the measure of Angle Q to the nearest degree.

Answers 1. 3. 2.