Question

If the hypotenuse of a right-angled is four times the length of the perpendicular drawn from the opposite vertex to it, then the difference of the two acute angles will be

• A. ${60}^{\circ }$
• B. ${15}^{\circ }$
• C. ${75}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

Consider the given figure.
sinC=DBBCsin⁡C=DBBC

=x4xcosC=x4xcos⁡C
Hence
sinC.cosC=14sin⁡C.cos⁡C=14
Or
2sinC.cosC=122sin⁡C.cos⁡C=12
sin2C=sin300sin⁡2C=sin⁡300
C=150C=150
Hence
A=900−150=750A=900−150=750
Hence
A−CA−C
=600=600