Answer:
The first blank: 65
The second blank: 24
The third blank: 16
The last blank is: 41
Step-by-step explanation:
The Phthagorean theorm is as follows: c^2=a^2+b^2
Where a and b are the legs of the triangle and c is the hypotenuse
To fill in the first blank space you need to find c, and it's given a and b: a=25 b=60
You substitute the known values into the equation of the Pythagorean theorm: c^2=25^2+60^2
And solve to find c
c^2=4225
c=
[tex] \sqrt{4225} [/tex]
c=65
The answer for the first blank
For the second blank you given a and c: a=7 c=25
Substitute the value into Pythagorean theorm:c^2=a^2+b^2
25^5=7^2+b^2
625=49+b^2
To solve b you got to subtract 49 to both sides
625-49=b^2
576=b^2
[tex] \sqrt{576} = b[/tex]
24=b
Which is your answer
For the third blank its given b and c: b=30 c=34
Substitute the value into Pythagorean theorm
c^2=a^2+b^2
34^2=a^2+30^2
Solve the exponential terms: 1156=a^2+900
Then you solve the variable that you need to find. In this case, you got to solve a^2 by subtracting 900 of both sides of the equation:1156-900=a^2
256=a^2
[tex] \sqrt{256 = a} [/tex]
16=a which is your answer
Finally your last blank,its given the values and b
a=9
b=40
Substitute the value into Pythagorean theorm
c^2=9^2+40^2
And solve for c
c^2=81+1600
c^2=1681
[tex]c = \sqrt{1681} [/tex]
Which gives you c=41 which is your answer
Let me know if this helps
