Answer:
[tex]\boxed {\boxed {\sf x \approx 30.9}}[/tex]
Step-by-step explanation:
This is a right triangle and we are looking for a missing side. We can use the Pythagorean Theorem to find x.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
In this triangle, the legs are 28 and 13 because they make up the right right angle. x is the hypotenuse because it is opposite the right angle.
[tex]a= 28 \\b= 13 \\c= x[/tex]
Substitute the values in.
[tex](28)^2+(13)^2=x^2[/tex]
Solve the exponents.
- (28)²=28*28=784
- (13)²=13*13=169
[tex]784+169=x^2[/tex]
Add the two numbers.
[tex]{953} =x^2\\[/tex]
We want to solve for x, which means we must isolate it.
The x is being squared. The inverse of a square is the square root, so take the square root of both sides of the equation.
[tex]\sqrt{953}=\sqrt{x^2} \\[/tex]
[tex]\sqrt{953} = x[/tex]
[tex]30.87069808=x[/tex]
Let's round to the nearest hundredth. The 7 in the thousandth place tells us to round the 8 to a 9.
[tex]30.9 \approx x[/tex]
x is about 30.9
