Answer:
x ≈ 4.5
Step-by-step explanation:
First, use the Pythagorean theorem to find the missing variable with side 8 and hypotenuse 10.
a² + b² = c²
a² + 8² = 10²
Square the variables
a² + 64 = 100
Subtract 64 from both sides.
a² = 36
Take the square root of both sides.
a = 6.
Now we can find the other triangle and we now know that one side is 4 and the hypotenuse is 6.
a² + b² = c²
x² + 4² = 6²
Square the variables.
x² + 16 = 36
Subtract 16 from both sides.
x² = 20
Square root. (refresh if you don't see this part.)
[tex]x=\sqrt{20}\\\text{Factor out a 2.}\\x=2\sqrt{5}[/tex]
Converted to decimal to the nearest tenth, the answer is
x = 4.5.
Now let's prove it.
[tex]a^2+b^2=c^2\\\text{Substitute variables.}\\(2\sqrt{5})^2+4^2=6^2\\\text{Factor the 2 in.}\\(\sqrt{20})^2+4^2=6^2\\\text{Square the variables.}\\20+16=36\\\text{Add.}\\36=36[/tex]
