we have that
1) triangle
a=3
b=5
c=?
applying the Pythagoras theorem
c²=a²+b²----> 3²+5²=34
c=√34
the answer part N 1) is c=√34
2) triangle
a=?
b=6
c=8
applying the Pythagoras theorem
c²=a²+b²----> a²=c²-b²-----> 8²-6²-------> a=√28
a=√28
the answer part N 2) is a=√28
3) triangle
a=?
b=3
c=√15
applying the Pythagoras theorem
c²=a²+b²----> a²=c²-b²-----> √15²-3²-------> a=√6
a=√6
the answer part N 3) is a=√6
4) triangle
a=5
b=6
c=13
c²--------> 13²=169
a²+b²----> 5²+6²=61
c²> (a²+b²)------------> the triangle is obtuse
5) triangle
a=5
b=12
c=13
c²--------> 5²=25
a²+b²----> 12²+13²=313
c²< (a²+b²)------------> the triangle is acute
6) triangle
a=9
b=11
c=13
c²--------> 9²=81
a²+b²----> 11²+13²=61
c²> (a²+b²)------------> the triangle is obtuse
N 8) the base of a ladder is placed 6 feet from a wall. If the top of the ladder is at a point 8 feet high, how long is the ladder?
we have that
a= 8 ft
b=6 ft
c=?
applying the Pythagoras theorem
c²=a²+b²----> 8²+6²-----> √100-------> c=10 ft
c=10 ft
the answer part N 8) is 10 ft
N 9) Amy laptop computer has a 15 inch diagonal and is 14 inch wide. Determine the height of the screem
we have that
a=?
b=14 in
c=15 in
applying the Pythagoras theorem
c²=a²+b²----> a²=c²-b²-----> 15²-14²-------> a=√29-----> a=5.39 in
a=5.39 in
the answer part N 9) is a=5.39 in
N 10)
we have that
a= 5
b=12
c=?
applying the Pythagoras theorem
c²=a²+b²----> 5²+12²-----> √169-------> c=13 blocks
c=10 ft
the answer part N 10) is 13 blocks