Question

Which expressions correctly represent the area of the triangle XYZ?

Answer 1

Answer:

Options (2) and Option (1)

Step-by-step explanation:

Area of the ΔXYZ = $\frac{1}{2}(\text{Base})(\text{Height})$

                              = $\frac{1}{2}(XZ)h$

                              = $\frac{1}{2}(18)h$

By applying sine rule in the ΔYPZ,

sin(38°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

sin(38°) = $\frac{h}{14}$

h = 14[sin(38°)]

Therefore, area of the given triangle = $\frac{1}{2}(18)(14)sin(38)$

By applying sine rule in ΔYPZ,

sin(58°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

sin(58°) = $\frac{h}{10}$

h = 10sin(58°)

Area of ΔXYZ = $\frac{1}{2}(18)(10)sin(58)$

Therefore, Options (2) and Option (1) are the correct options.