The pythagorean theorem is: a^2+ b^2= c^2
C is the hypotenuse, and a and b are the other sides of the triangle. You can identify the hypotenuse of the triangle as it being the longest side, and the one opposite the right angle.
I see you have done Question 1 and Question 2 correctly, so I’ll start with Question 3.
(But with question 1, you did the working out slightly wrong but still managed to get the right answer?! That confuses me, but well done!)
Question 3:
The hypotenuse is 4 and the other side length is 3. You can tell the side length that’s 4 is the hypotenuse because it’s the longest side, and the one opposite the right angle.
a^2+b^2=c^2 (c is the hypotenuse)
a^2+3^2=4^2
So: a^2=4^2-3^2
a^2=16-9
a^2= 7
a= root of 7, or 2.6 to one decimal place.
Answer: 2.6 (to one decimal place)
Question 5:
12 is the hypotenuse and 5 is another side length.
a^2+b^2= c^2
a^2+5^2=12^2
So: a^2= 12^2-5^2
a^2= 144-25
a^2= 119
a= root of 119, or 10.9 to one decimal place
Answer: 10.9 (to one decimal place)
I’ll skip question 5, and cover question 6:
Question 6:
This time the side lengths are 5 and 2, and the hypotenuse is missing.
a^2+b^2=c^2
5^2+2^2=c^2
25+4=c^2
29=c^2
c= root of 29, or 5.4 to one decimal place
Answer: 5.4 (to one decimal place)
Try to do the rest of the homework by yourself, with this to help you! (Unless someone else finishes the rest for you)
If you want to get better at something, you have to practice lots, which is why I’m not doing all of it.
(sorry if I’m wrong on any!!)
:)