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?

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?
Transcript text: Question 9 (Multiple Choice Worth 1 points) (05.01 MC) In the figure below, the length of segment $G E$ is $97 \sqrt{3}$ units and the length of segment $B G$ is 149 units. What is the length of segment $A C$ ? $52 \sqrt{3}$ 97 $52 \sqrt{2}$ 194 Question 10 (Multiple Choice Worth 1 points) (05.01 MC) In $\triangle P Q R$, what is the length of segment $Q R$ ?
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Solution

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Solution Steps

Step 1: Identify the given information
  • Length of segment GE = \( 97\sqrt{3} \) units
  • Length of segment BG = 149 units
  • We need to find the length of segment AC
Step 2: Analyze the triangle properties
  • 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.
Step 3: Use the properties of 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

The length of segment AC is 194 units.

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