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
a) Step 1: Find x. Given x = (5)/(13) and 0^ x 90^. Using the identity ^2 x + ^2 x = 1: ^2 x = 1 - ^2 x ^2 x = 1 - ((5)/(13))^2 ^2 x = 1 - (25)/(169) ^2 x = (169 - 25)/(169) ^2 x = (144)/(169) Since 0^ x 90^, x is positive: x = sqrt((144)/(169)) = (12)/(13) Step 2: Find x. Using the identity x = ( x)/( x): x = (5)/(13)(12)/(13) x = (5)/(12) Step 3: Substitute the values into the expression ( x - 2 x)/(2 x). Numerator: x - 2 x = (12)/(13) - 2((5)/(13)) = (12)/(13) - (10)/(13) = (2)/(13) Denominator: 2 x = 2((5)/(12)) = (10)/(12) = (5)/(6) Now, divide the numerator by the denominator: (2)/(13)(5)/(6) = (2)/(13) × (6)/(5) = (12)/(65) The value of the expression is (12)/(65). b) (i) Calculate |QP|. Step 1: Find the angles in PQR. The angle of elevation from