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 are the solutions for the problems: Problem 1 (Top Triangle): We have a right-angled triangle with a hypotenuse of 8 and an angle of 30^. We need to find the opposite side x and the adjacent side y. Step 1: Find x using the sine function. () = oppositehypotenuse (30^) = (x)/(8) x = 8 × (30^) x = 8 × (1)/(2) x = 4 Step 2: Find y using the cosine function. () = adjacenthypotenuse (30^) = (y)/(8) y = 8 × (30^) y = 8 × sqrt(3)2 y = 4sqrt(3) The values are: x = 4, y = 4sqrt(3) Problem 2 (Bottom Triangle): We have a right-angled triangle with a hypotenuse of 2 and an angle of 45^. We need to find the adjacent side x and the opposite side y. Step 1: Find x using the cosine function. () = adjacenthypotenuse (45^) = (x)/(2) x = 2 × (45^) x = 2 × sqrt(2)2 x = sqrt(2) Step 2: Find y using the sine function. () = oppositehypotenuse (45^) = (y)/(2) y = 2 × (45^) y = 2 × sqrt(2)2 y = sqrt(2) The values are: x = sqrt(2), y = sqrt(2) That's 2 down. 3 left today — send the next one.