Answer:
10.2 inches
Step-by-step explanation:
we know that
In this problem we have two cases
First case
The given lengths are two legs of the right triangle
so
![a=12\ in, b=15\ in](https://tex.z-dn.net/?f=a%3D12%5C%20in%2C%20b%3D15%5C%20in)
Applying the Pythagoras Theorem
Find the length of the hypotenuse
![c^{2}=a^{2} +b^{2}](https://tex.z-dn.net/?f=c%5E%7B2%7D%3Da%5E%7B2%7D%20%2Bb%5E%7B2%7D)
substitute
![c^{2}=12^{2} +15^{2}](https://tex.z-dn.net/?f=c%5E%7B2%7D%3D12%5E%7B2%7D%20%2B15%5E%7B2%7D)
![c^{2}=369](https://tex.z-dn.net/?f=c%5E%7B2%7D%3D369)
![c=19.2\ in](https://tex.z-dn.net/?f=c%3D19.2%5C%20in)
Second case
The given lengths are one leg and the hypotenuse
so
![a=12\ in, c=15\ in](https://tex.z-dn.net/?f=a%3D12%5C%20in%2C%20c%3D15%5C%20in)
Applying the Pythagoras Theorem
Find the length of the other leg
![b^{2}=c^{2} - a^{2}](https://tex.z-dn.net/?f=b%5E%7B2%7D%3Dc%5E%7B2%7D%20-%20a%5E%7B2%7D)
substitute
![b^{2}=15^{2} - 12^{2}](https://tex.z-dn.net/?f=b%5E%7B2%7D%3D15%5E%7B2%7D%20-%2012%5E%7B2%7D)
![b^{2}=81](https://tex.z-dn.net/?f=b%5E%7B2%7D%3D81)
![b=9\ in](https://tex.z-dn.net/?f=b%3D9%5C%20in)
Find the difference between the two possible lengths of the third side of the triangle
so
![19.2-9=10.2\ in](https://tex.z-dn.net/?f=19.2-9%3D10.2%5C%20in)
Answer:
The longest side of the ΔQRS is Side RS.
Step-by-step explanation:
Given: m∠R=65°, m∠S=35° we don't know what m∠Q is in ΔQRS.
To find m∠Q , we first need to know that all triangles have a sum of 180°. Since we are already given two angle measurements ( m∠R and m∠S) we can add them both measurements up which gives us 100°. Then we subtract 100 from the triangle sum which is 180° (180°-100°) and we are left with 80°. Which mean that m∠Q got to be 80°.
Now we know the all the angles measurements we can immediately find out which side is the longest. <u>To find the longest side its always lie opposite the largest angle which in this m∠Q (80°).</u> Which mean that side RS is the longest side in the triangle.