Among many other formulas, the area of a triangle is
[tex] S = \frac 1 2 a c \sin B [/tex]
where B is the angle between sides a and c.
[tex] S=\frac 1 2(10)(20) \sin 67^\circ \approx 92.05 \textrm{ sq cm}[/tex]
Answer: 92.05 sq cm, first choice
Bonus. Here's a formula for the area S of a triangle your teacher doesn't know:
[tex]16S^2 = 4a^2b^2 -(c^2-a^2-b^2)^2=(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)[/tex]
The area of a triangle exists at 92.05 sq cm.
The area of a triangle exists
S = (1/2) ac sin B
where B exists the angle between sides a and c.
[tex]$S=\frac{1}{2}(10)(20) \sin 67^{\circ}$[/tex]
[tex]\approx[/tex] 92.05 sq cm
The area of a triangle exists at 92.05 sq cm.
Therefore, the correct answer is option a) 92.05 sq cm.
To learn more about the area of a triangle
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