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Evaluate Sides of a 30-60-90 Triangle in Word Problems

In this lesson, students will learn how to evaluate the legs and hypotenuse of a 30-60-90 triangle, focusing on solving related word problems. We will identify the properties of the triangle, including the hypotenuse, short leg, and long leg, and use established formulas to find missing sides. Students will solve various examples, including finding the length of the altitude in an equilateral triangle. Mastery of these concepts will enhance understanding of right triangles and their applications.

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Evaluate Sides of a 30-60-90 Triangle in Word Problems

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  1. 60 3 30 Bell Ringer Find x and y X Y

  2. Objective • I can evaluate the legs and hypotenuse of a 30-60-90 triangle in word problems

  3. 60 30 Let’s identify the sides of a 30-60-90 triangle Hypotenuse Short Leg The longest side located across the right angle! The shortest side located across the 30 angle! Long Leg The side located across the 60 angle!

  4. 60 6 3 30 Formula Hypotenuse = 2*Short Leg Short Leg Long Leg= Short Leg* 3

  5. 60 X 30 Example 1 Find x and y. Solution: Which leg is given? Long Leg Long Leg= Y Long Leg = Short Leg * 5 3

  6. Example 2 If an equilateral triangle has side with length , find the length of the altitude.

  7. Solution

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