Math  /  Geometry

QuestionComplete the calculation for the area of the triangle below. area =12×9×11×=\frac{1}{2} \times 9 \times 11 \times \square \begin{tabular}{|l|l|l|} \hline cos51\cos 51^{\circ} & cos57\cos 57^{\circ} & cos72\cos 72^{\circ} \\ \hline sin51\sin 51^{\circ} & sin57\sin 57^{\circ} & sin72\sin 72^{\circ} \\ \hline \end{tabular} Watch video

Studdy Solution
Calculate the area:
Area=12×9×11×sin(57) \text{Area} = \frac{1}{2} \times 9 \times 11 \times \sin(57^\circ) =12×99×sin(57) = \frac{1}{2} \times 99 \times \sin(57^\circ) =49.5×sin(57) = 49.5 \times \sin(57^\circ)
Assuming sin(57)0.8387\sin(57^\circ) \approx 0.8387, we have:
Area49.5×0.8387 \text{Area} \approx 49.5 \times 0.8387 41.54 \approx 41.54
The area of the triangle is approximately 41.54 \boxed{41.54} square inches.

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