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 the solution for question 4: a) Step 1: Identify the known sides relative to angle . The side opposite to angle is AC = 2. The hypotenuse is AB = 4. Step 2: Use the sine ratio to find angle . () = OppositeHypotenuse = (AC)/(AB) = (2)/(4) = (1)/(2) Step 3: Calculate . = ((1)/(2)) = 30^ Step 4: Use the sum of angles in a triangle to find angle . The sum of angles in a triangle is 180^, and C = 90^. + + 90^ = 180^ + 30^ + 90^ = 180^ + 120^ = 180^ = 180^ - 120^ = 60^ The values of the angles are = 30^ and = 60^. b) Step 1: Use the Pythagorean theorem to find the length of side BC. AC^2 + BC^2 = AB^2 Step 2: Substitute the known values AC=2 and AB=4. 2^2 + BC^2 = 4^2 4 + BC^2 = 16 Step 3: Solve for BC^2. BC^2 = 16 - 4 BC^2 = 12 Step 4: Take the square root and simplify the surd. BC = sqrt(12) BC = sqrt(4 × 3) BC = sqrt(4) × sqrt(3) BC = 2sqrt(3) The length of side BC is 2sqrt(3). That's 2 down. 3 left today — send the next one.