1. **Problem 1: Find cos \(\theta\) and hypotenuse \(d\) in the right triangle.** Given base segments 6.2 cm and 3.8 cm, total base = \(6.2 + 3.8 = 10\) cm. Since \(\theta\) is at the left end of 6.2 cm segment, adjacent side = 6.2 cm. Hypotenuse \(d = 10\) cm. Calculate \(\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{6.2}{10} = 0.62\). 2. **Problem 2: Find missing numbers on number cards with median 6 and range 14.** Known numbers: 1, 5, ? , ? Range = max - min = 14, min = 1, so max = 1 + 14 = 15. Median of 4 numbers is average of 2nd and 3rd numbers = 6. Order numbers: 1, 5, ?, 15. Median = \(\frac{5 + ?}{2} = 6 \Rightarrow 5 + ? = 12 \Rightarrow ? = 7\). So missing numbers are 7 and 15. 3. **Problem 3: Find area of quadrilateral EFGH.** EH = 10 cm (vertical), HG = 11 cm (horizontal), FG = 5 cm (slant), right angles at E, H, F. Split quadrilateral into rectangle EHG and right triangle FGH. Area rectangle EHG = EH \(\times\) HG = 10 \(\times\) 11 = 110 cm\(^2\). Triangle FGH has base HG = 11 cm and height from F to HG can be found using Pythagoras: FG = 5 cm, FH vertical side, so height = \(\sqrt{FG^2 - FH^2}\) but FH is vertical side, given right angle at F. Since right angle at F, FH is vertical, so height = FH = 10 cm (same as EH). Area triangle FGH = \(\frac{1}{2} \times 11 \times 10 = 55\) cm\(^2\). Total area = 110 + 55 = 165 cm\(^2\). 4. **Problem 4: Solve equation \((5r + 7) \tan 47^\circ = 137.2\).** Calculate \(\tan 47^\circ \approx 1.0724\). Equation: \((5r + 7) \times 1.0724 = 137.2\). Divide both sides by 1.0724: \(5r + 7 = \frac{137.2}{1.0724} \approx 127.9\). Subtract 7: \(5r = 127.9 - 7 = 120.9\). Divide by 5: \(r = \frac{120.9}{5} = 24.2\). 5. **Problem 5: Find bearing from C to D on grid map.** Coordinates: C(2,4), D(7,7). Change in x = 7 - 2 = 5, change in y = 7 - 4 = 3. Bearing is angle clockwise from North. Calculate angle from East axis: \(\theta = \tan^{-1}(\frac{3}{5}) \approx 30.96^\circ\). Bearing from North = \(90^\circ - 30.96^\circ = 59.04^\circ\). Bearing rounded to nearest degree = 59\(^\circ\). 6. **Problem 6: Find best scale value A for Distance from home axis.** Max distance for Mia = 28 km, Leo = 52 km. To fit both on graph, scale A should be at least 52. Choose A = 60 for clear scale. 7. **Problem 7: Find best scale value A for Height (m) axis.** Heights: 28, 8, 48, 16. Max height = 48 m. Choose A = 50 for neat scale. **Final answers:** 1. \(\cos \theta = 0.62\), \(d = 10\) cm 2. Missing numbers: 7 and 15 3. Area quadrilateral = 165 cm\(^2\) 4. \(r = 24.2\) 5. Bearing from C to D = 59\(^\circ\) 6. Scale A for distance = 60 7. Scale A for height = 50