Answer:
The length of the missing side is 41.24 inches
Step-by-step explanation:
* Lets talk about the Pythagoras theorem
- It used in the right angle triangle
- The hypotenuse is the opposite side to the right angle and it's the
longest side in the triangle
- The two other sides in the right angle triangle are the legs of
the right angle
- If the length of the hypotenuse is c units and the lengths of the
two legs of the right angle area a and b
∴ a² + b² = c² ⇒ c = √(a² + b²)
* Now lets solve the problem
∵ The length of the hypotenuse = 45 inches
∵ The length of one legs of the right angle = 18 inches
- Lets use the Pythagoras theorem
∴ c² = a² + b²
∴ 45² = 18² + b² ⇒ subtract 18² from both sides
∴ b² = 45² - 18² = 2025 - 324 = 1701 ⇒ take square root for both sides
∴ b = √1701 = 41.24 inches
The answer is:
The missing side length is 41.24 inches.
Since we are working with a righ triangle, to solve this problem we can use the Pythagorean Theorem.
The Pythagorean Theorem states that:
[tex]Hypotenuse^{2}=(Side_{1})^{2}+(Side_{2})^{2}[/tex]
We are given that:
[tex]Hypotenuse=45in\\Side_{1}=18in[/tex]
So, isolating the missing side and substituting the given information, we have:
[tex](45in)^{2}=(18in)^{2}+(Side_{2})^{2}[/tex]
[tex](Side_{2})^{2}=(45in)^{2}-(18in)^{2}+[/tex]
[tex]\sqrt{(Side_{2})^{2}} =\sqrt{(45in)^{2}-(18in)^{2}}\\\\Side_{2}=\sqrt{2025in^{2}-324^{2}}=\sqrt{1701^{2}}\\\\Side_{2}=41.2431in=41.24in[/tex]
Have a nice day!
