Question

D) The size is 22.6 degrees, but how did they get it? ​

Answer 1

Answer:

Step-by-step explanation:

a). Since, BC is perpendicular to the plane FEDC, measure of angle BCD = 90°

By applying Pythagoras theorem in ΔBCD,

BD² = BC² + CD²

BD² = (10)² + (24)²

BD = √676

BD = 26 cm

B). Surface area of the wedge = Sum of all the surfaces of the wedge

Area of BCD = Area of AEF = $\frac{1}{2}(\text{Base})(\text{Height})$

                                             = $\frac{1}{2}(10)(24)$

                                             = 120 cm²

Area of CDEF = Length × Width

                       = ED × CD

                       = 26 × 24

                       = 624 cm²

Area of BCFA = 10 × 26 = 260 cm²

Area of ABDE = ED × BD

                       = 26 × 26

                       = 676 cm²

Total surface area of the wedge = 2(120) + 624 + 260 + 676

                                                     = 1800 cm²

C). Volume of the triangular prism = Area of the triangular base × Height

                                                         = (Area of BCD) × DE

                                                         = 120 × 26

                                                         = 3120 cm³

d). By applying sine rule in the right triangle BCD,

sin(∠BDC) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

                 = $\frac{BC}{BD}$

m(∠BDC) = $\text{sin}^{-1}(\frac{10}{26})$

               = 22.6°