The length of the brace required is 4.3m
What is sine rule?
In a ΔABC a, b and c are the sides and A, B and C are angles then,
[tex]\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
We can find the length, l as shown below:
Let AB=3m, BC=2m and AC=l
Let ∠A=25°
So, in ΔABC
[tex]\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}[/tex]
[tex]\frac{BC}{sinA}=\frac{AB}{sinC}[/tex]
[tex]\frac{2}{sin25}=\frac{3}{sinC}[/tex]
[tex]\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )[/tex]
∠C=39.34°
∠A+∠B+∠C=180°
∠B=180°-25°-39.34°
∠B=115.66°
[tex]\frac{BC}{sinA}=\frac{AC}{SinB}[/tex]
[tex]\frac{2}{sin25}=\frac{l}{sin(115.66)}[/tex]
[tex]l=\frac{2\times sin(115.66)}{sin25}[/tex]
l=4.2659
Rounding to nearest tenth of meter.
l=4.3m
Hence, the length of the brace required is 4.3m
Learn more about Sine Rule here:
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