Question

write an equation you could use to find the length of the missing side of each right triangle. then find the missing length. round to the nearest tenth if necessary. 7 a = 48 yd; b = 55 yd 8. a = 23 in.; b = 18 in. 9. b = 5.1 m; c = 12.3 m

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (the longest side) and $a$ and $b$ are the legs. If we need to find a leg, we can rewrite the formula as $a=\sqrt{c^{2}-b^{2}}$ or $b=\sqrt{c^{2}-a^{2}}$.

Step2: Solve for problem 7

Given $a = 48$ yd and $b = 55$ yd, we find the hypotenuse $c$. Using $c=\sqrt{a^{2}+b^{2}}$, we have $c=\sqrt{48^{2}+55^{2}}=\sqrt{2304 + 3025}=\sqrt{5329}=73$ yd. The equation is $c=\sqrt{48^{2}+55^{2}}$.

Step3: Solve for problem 8

Given $a = 23$ in and $b = 18$ in, we find the hypotenuse $c$. Using $c=\sqrt{a^{2}+b^{2}}$, we have $c=\sqrt{23^{2}+18^{2}}=\sqrt{529+324}=\sqrt{853}\approx29.2$ in. The equation is $c=\sqrt{23^{2}+18^{2}}$.

Step4: Solve for problem 9

Given $b = 5.1$ m and $c = 12.3$ m, we find the leg $a$. Using $a=\sqrt{c^{2}-b^{2}}$, we have $a=\sqrt{12.3^{2}-5.1^{2}}=\sqrt{(12.3 + 5.1)(12.3 - 5.1)}=\sqrt{17.4\times7.2}=\sqrt{125.28}\approx11.2$ m. The equation is $a=\sqrt{12.3^{2}-5.1^{2}}$.

Answer:

1. Equation: $c=\sqrt{48^{2}+55^{2}}$, Missing length: $c = 73$ yd
2. Equation: $c=\sqrt{23^{2}+18^{2}}$, Missing length: $c\approx29.2$ in
3. Equation: $a=\sqrt{12.3^{2}-5.1^{2}}$, Missing length: $a\approx11.2$ m