Presentation on theme: "Objective: To use the sine, cosine, and tangent ratios to determine missing side lengths in a right triangle. Right Triangle Trigonometry Sections 9.1."— Presentation transcript:
Objective: To use the sine, cosine, and tangent ratios to determine missing side lengths in a right triangle. Right Triangle Trigonometry Sections 9.1 and 9.2
IN A RIGHT TRIANGLE…. There are ratios we can use to determine side lengths. These ratios are constant, no matter what the lengths for the sides of the triangle are. These ratios are called trigonometric ratios. Three of the trigonometric ratios are: Sine (sin) Cosine (cos) Tangent (tan)
Example Use the triangle to write each ratio. 60 Z 87 63 Y X
If given the angle measure, you can use a trig function to find a missing side length of a right triangle. x 25 M L Find x. K 57° Which trig ratio relates the given angle, and the 2 sides?? Set up equation:
Example: To measure the height of a tree, Mrs. Shattuck walked 125 ft. from the tree, and measured a 32˚ angle from the ground to the top of the tree. Estimate the height of the tree.
Example: A 20 ft wire supporting a flagpole forms a 35˚ angle with the flagpole. To the nearest foot, how high is the flagpole?
Example: You are at the playground, and they just put in an awesome new slide. The slide is 25 ft long, and it creates a 57˚ angle with the ground. How high off the ground is the top of the slide?
If you need to find an angle in a right triangle given the side lengths, you use the inverse of the trig function: tan -1, sin -1, cos -1 tan -1 (.5) = x “The angle,x, whose tangent is.5” sin -1 (.7314)=x “The angle,x, whose sine is.7314” cos -1 (.5592)=x “The angle,x, whose cosine is.5592”
Fill in the blanks…. 1. cos __________ ≈.0175 2. sin __________ ≈.9659 3. tan___________ ≈.2309 In your calculator, enter cos -1 (.0175)
Find the indicated angle measures. 1. 2. S 41 47 T R 17 41 A How would you now find the measure of angle T??