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Which expressions correctly represent the area of the triangle XYZ?

Which expressions correctly represent the area of the triangle XYZ?-example-1
User MistaGreen
by
3.7k points

1 Answer

7 votes

Answer:

Options (2) and Option (1)

Explanation:

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

=
(1)/(2)(XZ)h

=
(1)/(2)(18)h

By applying sine rule in the ΔYPZ,

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

sin(38°) =
(h)/(14)

h = 14[sin(38°)]

Therefore, area of the given triangle =
(1)/(2)(18)(14)sin(38)

By applying sine rule in ΔYPZ,

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

sin(58°) =
(h)/(10)

h = 10sin(58°)

Area of ΔXYZ =
(1)/(2)(18)(10)sin(58)

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

Which expressions correctly represent the area of the triangle XYZ?-example-1
User Sinedsem
by
3.2k points