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: Use the co-function identity. Given that (90^ - ) = 0.8. We know the trigonometric identity (90^ - ) = . Therefore, we have: = 0.8 Step 2: Convert the decimal to a fraction. = (8)/(10) = (4)/(5) Recall that in a right-angled triangle, = adjacenthypotenuse. So, the adjacent side is 4 and the hypotenuse is 5. Step 3: Find the length of the opposite side using the Pythagorean theorem. Let the opposite side be y. (opposite)^2 + (adjacent)^2 = (hypotenuse)^2 y^2 + 4^2 = 5^2 y^2 + 16 = 25 y^2 = 25 - 16 y^2 = 9 y = sqrt(9) Since y represents a length, it must be positive: y = 3 So, the opposite side is 3. Step 4: Calculate . We know that = oppositeadjacent. = (3)/(4) The value of is (3)/(4). That's 2 down. 3 left today — send the next one.