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 to your math problems: 1. Rectangular field Step 1: Calculate the length of the diagonal of the rectangular field. The length (L) is 104 m and the breadth (B) is 76 m. The diagonal (D) can be found using the Pythagorean theorem: D = sqrt(L^2 + B^2) D = sqrt((104 m))^2 + (76 m)^2 D = sqrt(10816 m)^2 + 5776 m^2 D = sqrt(16592 m)^2 D ≈ 128.81 m Step 2: Calculate the distance from the centre spot to a corner. The distance from the centre spot to a corner is half the length of the diagonal. Distance = (D)/(2) Distance = 128.81 m2 Distance ≈ 64.41 m The distance from the centre spot to a corner is approximately 64.41 m. 2. School compound plan Assumption: The scale "2cm:10cm" is likely a typo and should be "2cm:10m" for a school compound plan. We will proceed with the assumption that 2 cm on the drawing represents 10 m in reality. This simplifies to a scale of 1 cm : 5 m. Step 1: Convert the actual dimensions to the drawing scale. The actual length is 160 m and the actual breadth is 106 m. The scale is 1 cm on the drawing for every 5 m in reality. Step 2: Calculate the length on the drawing. Length on drawing = 160 m × 1 cm5 m Length on drawing = (160)/(5) cm Length on drawing = 32 cm Step 3: Calculate the breadth on the drawing. Breadth on drawing = 106 m × 1 cm5 m Breadth on drawing = (106)/(5) cm Breadth on drawing = 21.2 cm The length on the drawing is 32 cm and the breadth on the drawing is 21.2 cm. 3. Triangle Step 1: Determine the size of angle g. The diagram shows a triangle with two sides marked with single dashes, indicating that these sides are equal in length. This means it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. One base angle is given as 63^. Therefore, the other base angle, g, must also be 63^. g = 63^ Step 2: Determine the size of angle h. The sum of angles in any triangle is 180^. So, we have: h + g + 63^ = 180^ Substitute the value of g: h + 63^ + 63^ = 180^ h + 126^ = 180^ h = 180^ - 126^ h = 54^ The size of g is 63^ and the size of h is 54^. Send me the next one 📸