hypotenuse hypotenuse opposite opposite adjacent adjacent

Finding a missing angle Finding a missing angle. (Figuring out which ratio to use and an inverse trig button.)

Ex: 1. Figure out which ratio to use. Find x Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. O 20 m 40 m A x Identify the given sides as H, O, or A. What trig ratio is this?

Ex: 2. Figure out which ratio to use. Find x Ex: 2 Figure out which ratio to use. Find x. Round to the nearest tenth. O H 15 m 50 m x Identify the given sides as H, O, or A. What trig ratio is this?

Ex. 3: Find . Round to the nearest degree. 17.2 9 A

Ex. 4: Find . Round to the nearest degree. 7 23 H

Ex. 5: Find . Round to the nearest degree. 200 O 400 H

Using a Calculator If you know the value of a specific trig ratio for an unknown angle, you can calculate the measure of the angle. For example, if for the triangle below 8 3 On most calculators written above the Sin, Cos and Tan buttons are: 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. This button will allow you to do the function above the button.

Using a Calculator On the calculator enter 0.375 the hit the “2nd” button and then the “Sin” button. The number 22.02 should be displayed. This is the angle that has a Sin value of 0.375 Then, that means 8 3 On a graphics calculators you will enter it just like it reads in the equation. Then you can calculate the angle value.

Problem-Solving Strategies Scenario 1) You are given 2 sides of the triangle. Find the other side and the two acute angles. OR 20 c 15 13 k 12 1A. Use the Pythagorean theorem to find the 3rd 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

Problem-Solving Strategies Scenario 1) You are given 2 sides of the triangle. Find the other side and the two acute angles. OR 20 c 15 13 k 12 2A. Use an inverse trig function to get an angle. Then use the sum of the angles = 180º to find the 3rd angle. 2B. Use a trig ratio using one of the two angles to get the 3rd side.

Problem-Solving Strategies 26 a Scenario 2) You are given an angle and a side. Find the other angle and the two other sides. 1A. Use 2 different trig ratios from the given angle to get each of the other two sides. 1B. Use the sum of the angles to get the 3rd angle.

Problem-Solving Strategies 26 a Scenario 2) You are given an angle and a side. Find the other angle and the two other sides. 2A. Use the sum of the angles to get the 3rd angle. 2B. Use 2 different trig ratios from the 3rd angle to get each of the other two sides.

Problem-Solving Strategies 24 25 7 Scenario 3) 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 Scenario 3) You are given all 3 sides of the triangle. Find the two non-right angles. 24 25 7 2A. Use a trig ratio to get one angle. 2B. Use the sum of angles to get the 3rd angle

Angle of Elevation/Depression Sometimes when we use right triangles to model real-life situations, we use the terms angle of elevation and angle of depression. If you are standing on the ground and looking up at a hot air balloon, the angle that you look up from ground level is called the angle of elevation. If someone is in the hot air balloon and looks down to the ground to see you, the angle that they have to lower their eyes, from looking straight ahead, is called the angle of depression. Balloon You Angle of depression Angle of elevation

Angle of Elevation/Depression If you look up 15º to see the balloon, then the person in the balloon has to look down 15º to see you on the ground. Angle of elevation = Angle of depression. Balloon Angle of depression = 15º Angle of elevation= 15º You Notice that in this situation, the one of the legs that forms the right angle is also the height of the balloon.

Draw a Picture When solving math problems, it can be very helpful to draw a picture of the situation if none is given. Here is an example. Find the missing sides and angles for Triangle FRY. Given that angle Y is the right angle, f = 68, and y = 88. 68 88 r The picture helps to visualize what we know and what we want to find!