For question one, you should memorise this rule, if c^2 is less than a^2 plus b^2, then the triangle is acute, if c^2 is equal to a^2 plus b^2, then the triangle is right. If c^2 is more than a^2 plus b^2, then the triangle is obtuse
1) the square root of 8^2 plus 24^2 is equal to 25, so the triangle is acute 2) the square root of 3.1^2 plus 4.1^2 is equal to 5.1, so the triangle is right 3) the square root of 0.11^2 plus 0.6^2 is equal to 0.61, so the triangle is right 4) the square root of 10^2 plus 39^2 is equal to 40, so the triangle is acute 5) the square root of 36^2 plus 77^2 is equal to 75, so the triangle is right 6) the square root of 65^2 plus 73^2 is equal to 97.74, but i don't know if your teacher wants the answer to the nearest whole number. If she/he wants it to the nearest whole number, then the triangle is obtuse.
Q13) square root of 10^2 plus 24^2 is 26 x is equal to 26
Q14) this time, we have the longest side, so we do square root of 13^2-12^2 which is five x is equal to five
Q15) supers root of 6^2-3^2m which is 5 x is equal to five
Q16) move twelve squared to the right side as a negative number
B squared is equal to 25
Square root of 25 is five
Q17) 30^2+16^2 is 1156
Square root of 1156 is 34
Q18) move eight squared to the other side as a negative number
B squared is equal to 36
Square root of thirty six is six
Q19) move a squared to other other side as a negative number
So it becomes b squared equals to c squared minus a squared
But they only want b by itself, not b squared, so we square root
So b is equal to c minus a
Q20) to find the hypotenuse, you do c squared equals to share root of a squared plus b squared
So,we do the square root of 24^2+7^2 p, which is 25
Q21) we have the hypotenuse (c), so we do square root of c squared minus a squared, which is 12
Q22) square root of 26^2 minus 10^2, which is 24
Q23) square root of 50^2 minus 48^2, which is 14
Q24) square root of 24^2 plus 45^2, which is 51 ( we plus, not minus because we aren't given the value of c)
I'm assuming the question means what integers, so let's figure it out.
Starting from 12, 12 squared is 144, or the square root of 144 is 12.
13 squared is 169, or the square root of 169 is 13.
14 squared is 196, or the square root of 196 is 14.
15 squared is 225, or the square root of 225 is 15.
Based on that list of numbers, we can determine that the square root of 199 lies between the square root of 196 and the square root of 225 -- aka 14 and 15.
