Questions: Question 9 (Multiple Choice Worth 1 points) (05.01 MC) In the figure below, the length of segment GE is 97√3 units and the length of segment BG is 149 units. What is the length of segment AC? 52√3 97 52√2 194 Question 10 (Multiple Choice Worth 1 points) (05.01 MC) In triangle PQR, what is the length of segment QR?

Solution Steps

• Length of segment GE = \( 97\sqrt{3} \) units
• Length of segment BG = 149 units
• We need to find the length of segment AC

• The triangle has angles of 45°, 60°, and 90°, indicating it is a right triangle.
• Segment GE is opposite the 60° angle, making it the longer leg in a 30°-60°-90° triangle.

• In a 30°-60°-90° triangle, the ratio of the sides opposite the 30°, 60°, and 90° angles are \( 1 : \sqrt{3} : 2 \).
• Given GE = \( 97\sqrt{3} \), which is opposite the 60° angle, the hypotenuse (opposite the 90° angle) is \( 2 \times 97\sqrt{3} / \sqrt{3} = 2 \times 97 = 194 \) units.

Final Answer