Can someone please help explain how to do this?

Use the triangle attached. Find the legnth of the missing side. If necessary, round to the nearest 10th. (This is for the smaller case red letters.) Thanks!

**1.** a=6, b=8

**2.** a=3, c=5

**3.** a=3/5, b=4/5

**4.** a=0.8, c=1

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using Pitagora theorem:

1. `c=sqrt(6^2+8^2)=10`

2. `c=sqrt(3^2+5^2)= 5,83095189484`

3. `c=sqrt(3/5+4/5)=1`

4. `c=sqrt(0.8^2+1^2)=1,28062484748`

Since the given figure is a right triangle, to solve for the missing side, apply the Pythagorean formula which is

`c^2=a^2+b^2`

where a and b are the legs of the triangle and c is the hypotenuse.

(1) a=6, b = 8

Plug-in the values of a and b.

`c^2=6^2+8^2`

`c^2=36+64`

`c^2=100`

Then, take the square root of both sides.

`sqrt(c^2)=+-sqrt100`

`c=+-10`

Since c represents the length of the hypotenuse, consider only the positive value.**Hence, the length of the missing side is 10.**

(2) a=3, c=5

Plug-in the values of a and c to the Pythagorean formula.

`5^2=3^2+b^2`

`25=9+b^2`

To isolate b, subtract both sides by 9.

`25-9=9-9+b^2`

`16=b^2`

Then, take the square root of both sides.

`+-sqrt16=sqrt(b^2)`

`+-4=b`

Again, consider only the positive value since b represents the length of the missing side of the triangle.**Thus, the length of the missing side of the triangle is 4.**

(For problem #3 and #4, please post them as separate questions. Or try to follow the steps above. )

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