Question

The area of $△QED=750.QE=48$ and $QD=52.$ To the nearest degree, what is the measure of the largest possible angle of $△QED$?

• A. 76
• B. 77
• C. 78
• D. 143
• E. 145

Answer 1

The correct option is D 143

The area of the triangle is given by the formula $A=\frac{1}{2}ab\sin \left(\theta \right)$.

Substituting $Area△QED=750$, $a=48$ and $b=52$ in the formula $A=\frac{1}{2}ab\sin \left(\theta \right)$ as shown below:

$750=\frac{1}{2}\left(48\right)\left(52\right)\sin \left(\theta \right)$

$\Rightarrow 2\times 750=2496\sin \left(\theta \right)\Rightarrow 1500=2496\sin \left(\theta \right)\Rightarrow \sin \theta =\frac{1500}{2496}\Rightarrow \sin \theta =0.61\Rightarrow \theta ={37}^0$

If $m\angle Q={37}^0$, then $\angle E$ would be the largest angle of triangle and that will measure $180-37={143}^0$.

Hence, the measure of the largest possible angle of $△QED$ is $143$.