某校课外活动小组,在距离湖面$7$米高的观测台$A$处,看湖面上空一热气球$P$的仰角为$37^{\circ}$,看$P$在湖中的倒影$P\’$的俯角为$53^{\circ}(P\’$为$P$关于湖而的对称点).请你算出这个热气球$P$距湖面得高度$PC$约为多少米?

注:$\sin 37^{\circ}\approx \dfrac{3}{5}$,$\cos 37^{\circ}\approx \dfrac{4}{5}$,$\tan 37^{\circ}\approx \dfrac{3}{4}$,$\sin 53^{\circ}\approx \dfrac{4}{5}$,$\cos 53^{\circ}\approx \dfrac{3}{5}$,$\tan 53^{\circ}\approx \dfrac{4}{3}$.