question_answer

The base angle of triangle are\[22{{\frac{1}{2}}^{o}}\]and\[122{{\frac{1}{2}}^{o}}\]If b is the base and h is the height of the triangle, then:

A)  \[b=2h\]            

B)  \[b=3h\]

C)  \[b=(1+\sqrt{3})h\]

D)         \[b=(2+\sqrt{3})h\]

E)  \[2b=3h\]

Correct Answer: A

Solution :

                In \[\Delta POR,\] \[\frac{PR}{\sin 90{}^\circ }=\frac{h}{\sin 67{{\frac{1}{2}}^{o}}}\]                               ?.(i) and in\[\Delta PQR,\] \[\frac{PR}{\sin 22{{\frac{1}{2}}^{o}}}=\frac{b}{\sin 45{}^\circ }\]                               ?.(ii) From Eqs. (i) and (ii) \[\frac{h}{b}=\frac{\sqrt{2}}{2}(\cos 45{}^\circ -\cos 90{}^\circ )\]                 \[=\frac{1}{2}\] \[\Rightarrow \]               \[2h=b\]