Calculating the legs of a right angle triangle

Question

Given- right angle triangle which is divided by its height, forming two triangles. The aria of one is S II=30.533(cm^2) c(hypotenuse)=65 (cm) The legs of the triangle need to be calculated. diagram of the triangle

Answer 1

From your given sketch
$$ \frac12 \cdot 65 \cos \alpha \cdot 65 \sin \alpha =S12$$

So this allows you to calculate $\alpha$

Proportion all the other sides by similar triangles using trigonometric ratios.