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 how to solve the problem: a) Calculate |MZ| Step 1: Identify the relevant right-angled triangle and trigonometric ratio. In the right-angled triangle YZM, we know the adjacent side |YZ| = 6 cm and the angle MYZ = 32^. We want to find the opposite side |MZ|. We use the tangent function. ( MYZ) = oppositeadjacent = (|MZ|)/(|YZ|) Step 2: Substitute the known values and solve for |MZ|. (32^) = (|MZ|)/(6 cm) |MZ| = 6 × (32^) |MZ| ≈ 6 × 0.624869 |MZ| ≈ 3.749214 cm Rounding to two decimal places: |MZ| ≈ 3.75 cm b) Hence write down the value of |XZ| and Calculate Step 3: Write down the value of |XZ|. Since M is the mid-point of XZ, the length of XZ is twice the length of MZ. |XZ| = 2 × |MZ| |XZ| = 2 × 3.749214 cm |XZ| ≈ 7.498428 cm Rounding to two decimal places: |XZ| ≈ 7.50 cm Step 4: Calculate . Consider the larger right-angled triangle YZX. We know the opposite side |XZ| ≈ 7.498428 cm and the adjacent side |YZ| = 6 cm for the angle XYZ. ( XYZ) = (|XZ|)/(|YZ|) ( XYZ) = 7.498428 cm6 cm ( XYZ) ≈ 1.249738 Step 5: Find the angle XYZ. XYZ = (1.249738) XYZ ≈ 51.329^ Step 6: Calculate . From the diagram, XYZ = XYM + MYZ. So, XYZ = + 32^. = XYZ - 32^ ≈ 51.329^ - 32^ ≈ 19.329^ Rounding to one decimal place: ≈ 19.3^ Send me the next one 📸