Problem Solving with Right Triangles Section 2

Lesson Objectives: You will be able to: 1.Find missing angles and sides using trigonometric ratios 2.Use the angle of elevation and angle of depression to solve real world problems

Lesson Objective # 1: Find missing angles and sides using trigonometric ratios

Solving Right Triangles With these six ratios, it is possible –to solve for any unknown side of the right triangle, if another side and an acute angle are known, or –to find the angle if two sides are known. Once upon a time, students had to rely on tables to look up these values. Now the sine, cosine, and tangent of an angle can be found on your calculator.

Using a Calculator Each trig ratios has a specific value for every angle. Using a calculator we can find the decimal values for the Sine, Cosine and Tangent ratios for any angle. Remember to make sure that the calculator is in Degree mode when calculating these values. This is shown as a D, or Deg in the display. For Example,

Inverse Trig Functions If sin is a trig function then sin -1 is an inverse trig function :inverse trig functions simply “undo” trig functions

If you know the value of a specific trig ratio for an unknown angle, you can calculate the measure of the angle. These are used to find the angle when you already know the value for the ratio. On the calculator there will be a button, sometimes it reads “2nd”, that will need to be pushed before you push the Sin, Cos or Tan button. Using a Calculator For example, if for the triangle 8 3 On most calculators written above the Sin, Cos and Tan buttons are:

Using a Calculator On the calculator enter the hit the “2nd” button and then the “Sin” button. On a graphics calculators you will enter it just like it reads in the equation. 8 3 The number should be displayed. This is the angle that has a Sin value of Then you can calculate the angle value. Then, that means

Using a Calculator Here are some examples

Finding Missing Sides You are given 2 sides of the triangle. Find the other side and the two non-right angles. 1A. Use the Pythagorean theorem to find the 3 rd side. 1B. Use an inverse trig function to get an angle. Then use that angle to calculate the 3rd angle. Sum of the angles = 180º OR 20 c k 12

2A. Use an inverse trig function to get an angle. Then use the sum of the angles = 180º to find the 3 rd angle. Finding Missing Sides Scenario 1) You are given 2 sides of the triangle. Find the other side and the two non-right angles. 2B. Use a trig ratio using one of the two angles to get the 3rd side. OR 20 c k 12

a b c To solve a right triangle means to find the missing lengths of its sides and the measurements of its angles.

Problem-Solving Strategies You are given all 3 sides of the triangle. Find the two non-right angles. 1. Use 2 different trig ratios to get each of the angles

Problem-Solving Strategies You are given all 3 sides of the triangle. Find the two non-right angles. 2A. Use a trig ratio to get one angle B. Use the sum of angles to get the 3 rd angle

10 15 c  Solve for the length of the hypotenuse and the angle, .

Wheel Chair Ramp The most common question when considering a portable wheelchair ramp is: what length of ramp is needed to achieve a safe, practical angle? The Americans with Disabilities Act standard states that a ramp's maximum incline should be no greater than a 6 degree angle.

Assignment Practice Worksheet