Question

Find the length of $AB$ in cm

• A. 39.25
• B. 81.96
• C. 46.32
• D. 85.34

Answer 1

The correct option is B 81.96

Given, $BC=30$
$\angle AED=\angle ABC=90$
Thus, $DE=BC=30$
Now, In $△ADE$
$\tan 45=\frac{AE}{DE}$
$1=\frac{AE}{30}$
$AE=30$
Now, In $△DBE$
$\tan 60=\frac{BE}{DE}$
$BE=30\sqrt{3}$
Now, $AB=BE+AE$
$AB=30\sqrt{3}+30$
$AB=81.96$ cm