Right Triangle Trigonometry Word Problems WarmUp Solve for
Right Triangle Trigonometry Word Problems
Warm-Up � Solve for x.
Warm-Up � Solve for x. Missing Side: Hypotenuse Trig Function: SINE Ratio: 12 sin 60=x x= 8√ 3
Word Problems � We can solve for a missing side in a right triangle using trig functions for word problems. � DON’T BE SCARED!!!! � The trick to solving word problems is to dissect the information and then create a trig ratio. � But first…….
Vocabulary � Angle of Elevation ◦ Angle that an observer would raise his or her line of sight above a horizontal line in order to see the object. angle of elevation � Angle of Depression ◦ If an observer were UP ABOVE and needed to look down, this would be the angle that the person would need to lower his or her line of sight. angle of depression
Angle of Elevation � Measured from the ground up. ◦ Like an elevator that only goes up. � It � In is always INSIDE the triangle. Example: You are looking straight ahead and you must raise (elevate) your eyes to see the top of the tree.
Angle of Depression � Always � In OUTSIDE the triangle. Example: You are standing at the top of the lighthouse and you are looking straight ahead. You must lower (depress) your eyes to see the boat in the water.
What do we do with an angle of depression that is OUTSIDE the triangle? 1. Find the angle adjacent to the angle inside the triangle. This is the complement of our angle. 2. Utilize the fact that the Angle of Depression=Angle of Elevation
Solving Trig Word Problems 1. Draw a Picture (Right Triangle) 1. Label the Given Parts 1. Set Up the Trig Ratios and Solve
Practice 1. A tree casts a shadow 21 m long. The angle of elevation of the sun is 60. What is the height of the tree? � Draw a picture � Label � Trig Ratio: 21 tan 60=x x= 36. 37 meters
More Practice…. � From the top of a tower, the angle of depression to a stake on the ground is 60. the top of the tower is 80 feet above the ground. How far is the stake from the food of the tower?
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