2. Sample answer: Draw a line using a ruler. Then use a protractor to measure a 90° angle. On one ray mark a 2 cm length, and at that endpoint use the protractor to measure a 30° angle toward the other ray. Where this ray intersects the other ray should form a 60° angle, completing the 30°-60°-90° triangle with sides 2 cm, 2 Ï 3 w cm, and a hypotenuse of 4 cm. 3. The diagonal is twice as long as its width w ,so the diagonal forms a 30°-60°-90° triangle with the length , and the width w . Then the length of the rectangle is Ï 3 w times the width, or , 5 Ï 3 w w . 4. The triangle is a 45°-45°-90° triangle. The legs are congruent, so x 5 3. The length of the hypotenuse is Ï 2 w times the length of the leg, so y 5 3 Ï 2 w . 5. The triangle is a 45°-45°-90° triangle. The legs are congruent, so x 5 y . The length of the hypotenuse is Ï 2 w times the length of the leg. 10 5 ¬ x Ï 2 w } Ï 10 2 w } 5 ¬ x } Ï 10 2 w } ? } Ï Ï 2 w 2 w } 5 ¬ x } 10 2 Ï 2 w } 5 ¬ x 5
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