This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to solve question 34: Step 1: Identify the known values and the unknown. We have a right-angled triangle with an angle of 30^. The hypotenuse (the side opposite the right angle) is 8 cm. We need to find the length of the side opposite the 30^ angle, which is labeled x. We are given (30^) = 0.5. Step 2: Apply the sine trigonometric ratio. The sine of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse: () = oppositehypotenuse Substitute the given values into the formula: (30^) = (x)/(8 cm) Step 3: Substitute the value of (30^) and solve for x. We are given that (30^) = 0.5. 0.5 = (x)/(8 cm) To find x, multiply both sides of the equation by 8 cm: x = 0.5 × 8 cm x = 4 cm Step 4: Compare the result with the given options. The calculated value for x is 4 cm. The options are: (A) 5.00 m (B) 4.50 m (C) 4.62 m (D) 4.00 m Although the unit in option (D) is meters, the numerical value 4.00 matches our calculated value of 4. Given the context of the diagram showing sides in centimeters, it is highly probable that the unit in option (D) is a typo and should be centimeters. The correct option is (D). The value of x is 4.00 cm. That's 2 down. 3 left today — send the next one.