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
Step 1: Find the third angle of the triangle. The sum of angles in a triangle is 180^. Let the unknown angle be . = 180^ - (60^ + 30^) = 180^ - 90^ = 90^ This means the triangle is a right-angled triangle. Step 2: Identify the sides and angles in relation to the right-angled triangle. Let the angle opposite side x be 30^. Let the angle opposite the side 8 cm be 90^. This means 8 cm is the hypotenuse. We need to find x, which is the side opposite the 30^ angle. Step 3: Use the sine function to find x. The sine of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the hypotenuse. (angle) = oppositehypotenuse For the 30^ angle: (30^) = (x)/(8) We know that (30^) = (1)/(2). (1)/(2) = (x)/(8) Step 4: Solve for x. Multiply both sides by 8: x = 8 × (1)/(2) x = 4 The unit for x is cm. The value of x is 4 cm. x = 4 cm