1. Special Right Triangles EQ: How do you use the properties of special right triangles in real world applications? M2 Unit 2: Day 2

2. 1. The logo on the recycling bin at the right resembles an equilateral triangle with side lengths of 6 centimeters. What is the approximate height of the logo? SOLUTION 30 - 60 - 90 o o o Draw the equilateral triangle described. Its altitude forms the longer leg of two triangles. The length h of the altitude is approximately the height of the logo. h = 3 5.2 cm 3 longer leg = shorter leg 3

3. 2. The side length of an equilateral triangle is 5 cm. Find the length of an altitude of the triangle.

4. 3. You have a guitar pick that resembles an equilateral triangle. It has a perimeter of 96 mm. What is the approximate height of the pick?

5. Sketch the figure that is described. Find the requested length. Round decimals to the nearest tenth. 4. The perimeter of an equilateral triangle is 60 in. Find the length of an altitude of the triangle.

6. 5. A baseball diamond is a square. The distance from base to base is 90 feet. To the nearest foot, how far does the second baseman throw a ball to home plate? Label the bases. What is the length of the diagonal? Draw a square and label the sides 90 feet. Home 1st 2nd 3rd The distance from second base to home plate is about 127 feet.

7. 6. The perimeter of a square is 36 in. Find the length of a diagonal.

8. 7. The diagonal of a square is 26 in. Find the length of a side.

9. 8. A point on the edge of a symmetrical canyon is 4500 feet above a river that cuts through the canyon floor. The angle of depression from each side of the canyon to the canyon floor is 60°. a) Find the distance across the canyon. b) Find the length of the canyon wall (from the edge to the river). c) Is it more or less than a mile across the canyon? (5280 feet 1 mile) less

10. 9. A light pole is 30 ft high and is stabilized by a guy wire. A 30 degree angle is formed by the wire and the pole.  Find the length of the wire.  Find the distance from the base of the pole to the point where the wire meets the ground.  What is the angle measure formed by the wire and the ground?

11. 10. Billy plans to clean out the gutters at his house. He leans a 12 foot ladder against the wall. The ladder forms a 45 degree angle with the wall.  What is the angle formed at this point?  What type of triangle is formed?  How far is the bottom of the ladder from the bottom of the wall?

12. The side lengths of a triangle are given. Determine whether it is a 45 o -45 o -90 o triangle, a 30 o -60 o -90 o triangle, or neither. 11. 12. The shorter leg is 6 The longer leg is The hypotenuse is 12. 30 o -60 o -90 o triangle If the side was It would be a 45 o -45 o -90 o neither

13.  Homework:  page 154 #23a  page 155 #4-12 even  Page 156 #17, 19-21 all