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 29(a): Step 1: Find AC using the Pythagorean theorem. In the right-angled triangle ABC, with the right angle at B: AC^2 = AB^2 + BC^2 AC^2 = (12 cm)^2 + (5 cm)^2 AC^2 = 144 cm^2 + 25 cm^2 AC^2 = 169 cm^2 AC = sqrt(169 cm)^2 AC = 13 cm The length of AC is 13 cm. Step 2: Find the value of (1 + ^2 ). From the triangle, is the angle at C. First, find : = oppositeadjacent = (AB)/(BC) = (12)/(5) Now, substitute this into the expression: 1 + ^2 = 1 + ((12)/(5))^2 1 + ^2 = 1 + (144)/(25) 1 + ^2 = (25)/(25) + (144)/(25) 1 + ^2 = (169)/(25) The value of (1 + ^2 ) is (169)/(25). Step 3: Find the Area of ABC. The area of a right-angled triangle is given by: Area = (1)/(2) × base × height Area = (1)/(2) × BC × AB Area = (1)/(2) × 5 cm × 12 cm Area = (1)/(2) × 60 cm^2 Area = 30 cm^2 The area of ABC is 30 cm^2. Step 4: Find . From the triangle, is the angle at C. = oppositehypotenuse = (AB)/(AC) Using the value of AC from Step 1: = 12 cm13 cm = (12)/(13) The value of is (12)/(13). Send me the next one 📸