Question

if the length of the tank is 7, the width is 4, and the height is 5, what is the diagonal of the base? $a^{2}+b^{2}=c^{2}$ once the diagonal is out, what two angles are created? $sin=\frac{opp}{hyp}, cos=\frac{adj}{hyp}, tan=\frac{opp}{adj}$

Explanation:

Step1: Apply Pythagorean theorem for base diagonal

The base has length $l = 7$ and width $w=4$. For a rectangle (base of the tank), the diagonal $d$ of the base is found using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 7$ and $b = 4$. So $d=\sqrt{7^{2}+4^{2}}=\sqrt{49 + 16}=\sqrt{65}\approx 8.06$.

Step2: Identify angles with trigonometric relations

The two non - right angles in the right - triangle formed by the length, width and base diagonal are $\theta_1$ and $\theta_2$. One angle $\theta_1$ has $\sin\theta_1=\frac{4}{\sqrt{65}}$, $\cos\theta_1=\frac{7}{\sqrt{65}}$, $\tan\theta_1=\frac{4}{7}$ and the other angle $\theta_2$ has $\sin\theta_2=\frac{7}{\sqrt{65}}$, $\cos\theta_2=\frac{4}{\sqrt{65}}$, $\tan\theta_2=\frac{7}{4}$.

Answer:

The diagonal of the base is $\sqrt{65}\approx8.06$. The two angles are $\arctan(\frac{4}{7})$ and $\arctan(\frac{7}{4})$.