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: Calculate . Using the sine rule: (8)/( 47^) = (10)/( ) Rearrange to solve for : = (10 47^)/(8) = (10 × 0.73135)/(8) = (7.3135)/(8) ≈ 0.9141875 Rounding to four decimal places as in the image: ≈ 0.9142 Step 2: Calculate . Take the inverse sine of the value: = (0.9141875) ≈ 66.090^ Rounding to two decimal places as in the image: ≈ 66.09^ Step 3: Calculate the third angle of the triangle. The sum of angles in a triangle is 180^. Third angle = 180^ - 47^ - 66.09^ Third angle = 180^ - 113.09^ Third angle = 66.91^ Step 4: Calculate x using the sine rule. Using the sine rule with the third angle and the known side: (x)/( 66.91^) = (8)/( 47^) Rearrange to solve for x: x = (8 66.91^)/( 47^) x = (8 × 0.92000)/( 47^) x = (7.36000)/(0.73135) x ≈ 10.0635 Rounding to two decimal places as in the image: x ≈ 10.06 km The steps and calculations provided in the image are correct. The final answer is 10.06 km. Send me the next one 📸