2 The figure represents a triangular prism with \( A B=A C=10 \mathrm{~cm} \) and \( \mathrm{BAC}=70^{\circ} \). 2.1 Calculate the area of \( \triangle \mathrm{ABC} \). 2.2 Calculate the length of BC . 2.3 Calculate the height CF of the prism if

To find the area of triangle \(ABC\), we can use the formula for the area of a triangle given two sides and the included angle: \[ \text{Area} = \frac{1}{2} \times AB \times AC \times \sin(BAC) \] Substituting the values: \[ \text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 10 \, \text{cm} \times \sin(70^{\circ}) \approx 48.3 \, \text{cm}^2 \] Now moving on to find the length of \( BC \) using the Law of Cosines: \[ BC^2 = AB^2 + AC^2 - 2 \times AB \times AC \times \cos(BAC) \] Substituting in our values: \[ BC^2 = 10^2 + 10^2 - 2 \times 10 \times 10 \times \cos(70^{\circ}) \] \[ BC^2 \approx 100 + 100 - 200 \times 0.342 = 100 + 100 - 68.4 \approx 131.6 \] \[ BC \approx 11.5 \, \text{cm} \] For part 2.3, if you provide additional information about the prism, such as the base and how it's oriented, I can help you calculate the height \( CF \) of the prism!