Question

In an acute angled triangle ABC, D,E and F are the feets of perpendiculars from A,B and C respectively and H is the orthocenter.
$\mathrm{If}\sin A=\frac{3}{5}\mathrm{and}\mathrm{BC}=39,\mathrm{then}\mathrm{length}\mathrm{of}\mathrm{AH}=$
.

• A. 52
• B. 65
• C. 26
• D. 39

Answer 1

The correct option is A 52

$\mathrm{Given},\sin A=\frac{3}{5}\Rightarrow \cos A=\frac{4}{5}\mathrm{Also},a=39\therefore \frac{a}{\sin A}=2R\mathrm{or}\frac{39\times 5}{3}=2R\mathrm{or}2R=65\Rightarrow \mathrm{AH}=2R\cos A=65\times \frac{4}{5}=52$