help if you are smart and nice

Hello! I tried to explain a little so that you can understand. If you have questions, let me know! I hope this helps!

1)

a)The legs are g, p, and j. The hypotenuse is the leg opposite of the right angle, so the hypentenuse in this problem is g.

b) The legs are n, d, and r. The hypotenuse is d.

thank you so much

1. a) & b) remember that the hypotenuse is the longest side of a right triangle or the side that isn't next to the right angle, and the rest are legs. 

2. a), b), and c) I'm assuming that you know the pythagorean theorem. remember that it is \(a^2+b^2=c^2\), when c is the hypotenuse. Now you can solve them :)

Hints: a) \(?\) isn't next to the right angle, so it's the hypotenuse. Therefore, \(c^2= 8^2+5^2\), and \(c= \sqrt{8^2+5^2}\). 

b) and c) both of the \(?\) are next to the right angle, so it's a leg. Thus, \(b= \sqrt{c^2-a^2}\) for both. (it doesn't really matter whether the \(?\) is a or b)

3. a) \(h^2=7^2+3^2\), so \(h= \sqrt{7^2+3^2}\).

b) \(b=\sqrt{8^2-6^2}\)

c)\(h=\sqrt{12^2+10^2}\)

d) it's actually a triangle you should memorize, which is \(5-12-13\), so you know what \(l\) is.

4. a), b), and c) again, it's almost the same as above.

a) \(?=\sqrt{9^2-6^2}\)

b) \(?=\sqrt{10^2+12^2}\)

c) \(?=\sqrt{25^2-22^2}\)

Hope this helps! 

2) 

a) To solve this problem, you'd use a²+b²=c², where c is the hypotenuse.

8²+5²=c²         solve

64+25=c²         add

c²=89             square root each side

c=√89

b) Use a²+b²=c² again.

a²+3²=4²        solve

a²+9=16         subtract

a²=7               square root each side

a=√7

c) Use a²+b²=c² again.

a²+8²=15²      solve

a²+64=225     subtract

a²=161           square root each side

a=√161

thank you all 4 your help, I appreciate u so much!!!

don't worry u r all smart and nice