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EXAMPLE 4

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?.

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EXAMPLE 4

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  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? 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. o o o 30 - 60 - 90 EXAMPLE 4 Find the height of an equilateral triangle Logo SOLUTION

  2. h = 3 5.2 cm 3 3 EXAMPLE 4 Find the height of an equilateral triangle longer leg = shorter leg

  3. o o o Find lengths in a 30-60-90triangle 3 3 3 3 3 3 3 3 3 3 longer leg = shorter leg 9 = x Triangle Theorem 9 = x Divide each side by Multiply numerator and denominator by 9 = x o o o 30 - 60 - 90 9 = x 3 3 = x EXAMPLE 5 Find the values of xand y. Write your answer in simplest radical form. Find the value of x. STEP 1 Multiply fractions. Simplify.

  4. o o o Find lengths in a 30-60-90triangle longer leg = 2 shorter leg 3 3 Triangle Theorem y = 2 3 = 6 o o o 30 - 60 - 90 EXAMPLE 5 STEP 2 Find the value of y. Substitute and simplify.

  5. The body of a dump truck is raised to empty a load of sand. How high is the 14 foot body from the frame when it is tipped upward at the given angle? o o a. b. 60 angle 45 angle o a. When the body is raised 45 above the frame, the height his the length of a leg of a triangle. The length of the hypotenuse is 14 feet. o o o 45 - 45 - 90 EXAMPLE 6 Find a height Dump Truck SOLUTION

  6. 14 = h 14 = h Divide each side by 2 2 o When the angle of elevation is 45, the body is about 9feet 11 inches above the frame. 2 o b. 9.9 h When the body is raised 60, the height h is the length of the longer leg of a triangle. The length of the hypotenuse is 14 feet. o o o o o o 45 - 45 - 90 30 - 60 - 90 EXAMPLE 6 Find a height Triangle Theorem Use a calculator to approximate.

  7. longer leg=2shorter leg 14 =2s 3 3 longer leg = shorter leg Triangle Theorem Triangle Theorem h =7 h 12.1 o When the angle of elevation is 60, the body is about 12feet 1 inch above the frame. o o o o o o 30 - 60 - 90 30 - 60 - 90 EXAMPLE 6 Find a height Substitute. 7 =s Divide each side by 2. Substitute. Use a calculator to approximate.

  8. 3 3 3 Triangle Theorem longer leg = shorter leg x = o o o x 3 = 30 - 60 - 90 for Examples 4, 5 and 6 GUIDED PRACTICE Find the value of the variable. SOLUTION Substitute. Simplify.

  9. 3 3 Triangle Theorem o o o 30 - 60 - 90 h =2 h = 2 for Examples 4, 5 and 6 GUIDED PRACTICE Find the value of the variable. SOLUTION All side are equal, therefore it is an equilateral triangle a 30° - 60° - 90° triangle can be found by dividing an equilateral triangle in half longer leg=2shorter leg Substitute. Simplify.

  10. Triangle Theorem Hypotenuse =2 shorter leg = 14 2 x x = o o o 14 2 x 30 - 60 - 90 = 7 for Examples 4, 5 and 6 GUIDED PRACTICE Find the value of the variable. What If?In Example 6, what is the height of the body of the dump truck if it is raised 30° above the frame? 7. SOLUTION Substitute. Divide both sides by 2 Simplify.

  11. ANSWER The shorter side is adjacent to the 60° angle, the longer side is adjacent to the 30° angle. for Examples 4, 5 and 6 GUIDED PRACTICE Find the value of the variable. In a 30°- 60°- 90° triangle, describe the location of the shorter side. Describe the location of the longer side? 8.

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