Question

Please find x! Thank you, only if you know!

Answer 1

`\boxed {\boxed {\sf x \approx 23.49 \ cm }}`

Explanation:

This is a right triangle (the small square in the corner signifies a 90 degree angle), so Pythagorean Theorem can be used.

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

where a and b are the legs of the triangle and c is the hypotenuse. In this triangle, 17 and x are the legs because they form the right angle. 29 in the hypotenuse because it is opposite the right angle.

`a= 17 \\b=x \\c= 29`

`17^(2) + x^(2) =29^(2)`

Solve the exponents.

• 17²=17*17=289
• 29²= 29*29=841

`289+x^(2) =841`

289 is being added to x and the inverse is subtraction. Subtract 289 from both sides to isolate the variable.

`289-289+ x^(2) =841-289\\x^(2) =552`

x is being squared and the inverse is a square root. Take the square root of both sides of the equation.

`\sqrt {x^(2) }=\sqrt {552}`

`x=23.4946802489`

Let's round to the nearest hundredth. The 4 in the thousandth place tells us to leave the 9.

`x \approx 23.49`

x is approximately 23.49 centimeters.