Question

If we construct a triangle $\Delta ABC$ such that $\angle C={90}^o$ and $\angle A=\frac{2}{3}\angle B$. Then find the measures of $\angle A,\angle B$.

Answer 1

Given for the $\Delta ABC$ we've $\angle C={90}^o$.

Then $\angle A+\angle B={90}^o$

or, $\frac{2}{3}\angle B+\angle B={90}^o$

or, $\frac{5}{3}\angle B={90}^o$

or, $\angle B={54}^o$.

Then $\angle A={36}^o$.