Short Leg:Long Leg:Hypotenuse. 30-60-90 Right Triangle 1 2 30 60 This is our reference triangle for the 30-60-90 triangle. We will use a reference triangle.

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Presentation transcript:

Short Leg:Long Leg:Hypotenuse

Right Triangle This is our reference triangle for the triangle. We will use a reference triangle to set up a proportion then solve.

x 24 Solve for x and y Ex: 2 2a a a√3y

Leg:Leg:Hypotenuse

x 3 45 EX: 3 Solve for x a√2 a a

opposite hypotenuse adjacent hypotenuse opposite adjacent

Finding a side. (Figuring out which ratio to use and getting to use a trig button.)

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. 20 m x tan 2055 ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 2 Find the missing side. Round to the nearest tenth. 80 ft x tan 8072 =  ( ) ) Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 3 Find the missing side. Round to the nearest tenth. 283 m x Shrink yourself down and stand where the angle is. Now, figure out which trig ratio you have and set up the problem.

Ex: 4 Find the missing side. Round to the nearest tenth. 20 ft x

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

Angle of Elevation/Depression Balloon You Angle of depression Angle of elevation 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.

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. Notice that in this situation, the one of the legs that forms the right angle is also the height of the balloon. Angle of elevation = Angle of depression. Balloon You Angle of depression = 15º Angle of elevation= 15º

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 = r The picture helps to visualize what we know and what we want to find!