Question

find the length of the hypotenuse in the following triangles. round answers to the nearest tenth. use the formula ( c^{2}=a^{2}+b^{2} ).
5)

( c^{2}=a^{2}+b^{2} )
( c^{2}=\frac{2}{-}+\frac{2}{-} )
( c^{2}=\frac{}{-}+\frac{}{-} )
( c^{2}=\frac{}{-} )
( sqrt{c^{2}}=sqrt{-} )
( c= )
6)

( c^{2}=a^{2}+b^{2} )
( c^{2}=\frac{2}{-}+\frac{2}{-} )
( c^{2}=\frac{}{-}+\frac{}{-} )
( c^{2}=\frac{}{-} )
( sqrt{c^{2}}=sqrt{-} )
( c approx )
7)

( c^{2}=a^{2}+b^{2} )
( c^{2}=\frac{2}{-}+\frac{2}{-} )
( c^{2}=\frac{}{-}+\frac{}{-} )
( c^{2}=\frac{}{-} )
( sqrt{c^{2}}=sqrt{-} )
( c approx )
8)

( c^{2}=a^{2}+b^{2} )
( c^{2}=\frac{2}{-}+\frac{2}{-} )
( c^{2}=\frac{}{-}+\frac{}{-} )
( c^{2}=\frac{}{-} )
( sqrt{c^{2}}=sqrt{-} )
( c approx )

Explanation:

Step1: Substitute values into formula

For problem 5:
$$c^{2}=6^{2}+8^{2}$$
For problem 6:
$$c^{2}=7^{2}+7^{2}$$
For problem 7:
$$c^{2}=3^{2}+9^{2}$$
For problem 8:
$$c^{2}=6^{2}+7^{2}$$

Step2: Calculate squares

For problem 5:
$$c^{2}=36 + 64$$
For problem 6:
$$c^{2}=49+49$$
For problem 7:
$$c^{2}=9 + 81$$
For problem 8:
$$c^{2}=36+49$$

Step3: Sum the values

For problem 5:
$$c^{2}=100$$
For problem 6:
$$c^{2}=98$$
For problem 7:
$$c^{2}=90$$
For problem 8:
$$c^{2}=85$$

Step4: Take square - root

For problem 5:
$$\sqrt{c^{2}}=\sqrt{100}$$
For problem 6:
$$\sqrt{c^{2}}=\sqrt{98}$$
For problem 7:
$$\sqrt{c^{2}}=\sqrt{90}$$
For problem 8:
$$\sqrt{c^{2}}=\sqrt{85}$$

Step5: Find the value of \(c\)

For problem 5:
$$c = 10$$
For problem 6:
$$c=\sqrt{98}\approx9.9$$
For problem 7:
$$c=\sqrt{90}\approx9.5$$
For problem 8:
$$c=\sqrt{85}\approx9.2$$

Answer:

1. \(c = 10\)
2. \(c\approx9.9\)
3. \(c\approx9.5\)
4. \(c\approx9.2\)