Question

solve for a and b answer attempt 1 out of 3 a = b =

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $a:b:c = 1:1:\sqrt{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs.

Step2: Set up the equation for the hypotenuse

We know that $c = 7\sqrt{3}$, and $c=\sqrt{2}a$ (since $a = b$ in a 45 - 45 - 90 triangle). So, $\sqrt{2}a=7\sqrt{3}$.

Step3: Solve for $a$ and $b$

To find $a$, we solve the equation $\sqrt{2}a = 7\sqrt{3}$ for $a$. Divide both sides by $\sqrt{2}$: $a=\frac{7\sqrt{3}}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{7\sqrt{3}\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{7\sqrt{6}}{2}$. Since $b = a$ in a 45 - 45 - 90 triangle, $b=\frac{7\sqrt{6}}{2}$.

Answer:

$a=\frac{7\sqrt{6}}{2}$
$b=\frac{7\sqrt{6}}{2}$