Answer:
[tex]\boxed {\boxed {\sf x\approx 7.3}}[/tex]
Step-by-step explanation:
The triangle has a small square in the corner representing a 90 degree angle. This is a right triangle so we can use the Pythagorean Theorem to solve for the sides.
[tex]a^2+b^2=c^2[/tex]
In this equation, a and b are the legs and c is the hypotenuse.
x and 8.5 are the legs because they make up the right angle. 11.2 is the hypotenuse because it is opposite the right angle.
Substitute the values into the formula.
[tex]x^2+(8.5)^2=(11.2)^2[/tex]
Solve the exponents.
- (11.2)²= 11.2*11.2= 125.44
[tex]x^2+72.25 =125.44[/tex]
Solve for x by isolating the variable. 72.25 is being added, so we subtract 72.25 from both sides because subtraction is the inverse operation of addition.
[tex]x^2+72.25-72.25 = 125.44-72.25[/tex]
[tex]x^2=125.44-72.25[/tex]
[tex]x^2=53.19[/tex]
x is being squared, so we take the square root of both sides.
[tex]\sqrt{x^2}=\sqrt {53.19}[/tex]
[tex]x=\sqrt{53.19[/tex]
[tex]x=7.29314746869[/tex]
Round to the nearest tenth. The 9 in the hundredth place tells us to round the 2 up to a 3.
[tex]x \approx 7.3[/tex]
The unknown side, x, is approximately 7.3
