Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

One of the legs of a right triangle measures 9 cm and the other leg measures 11 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

Sagot :

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf 14.2 \ cm}}[/tex]

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem to solve for the sides.

[tex]a^2+b^2=c^2[/tex]

where a and b are the legs and c is the hypotenuse. In this triangle, we know the legs are 9 centimeters and 11 centimeters, or:

  • a= 9 cm
  • b= 11 cm

Substitute these values into the formula.

[tex](9 \ cm)^{2} +(11 \ cm)^{2} =c^{2}[/tex]

Solve the exponents.

  • (9 cm)²= 9 cm*9 cm=81 cm²

[tex]81 \ cm^{2} +(11 \ cm)^{2} =c^{2}[/tex]

  • (11 cm)²= 11 cm*11 cm= 121 cm²

[tex]81 \ cm^{2} +121 cm^{2} =c^{2}[/tex]

Add the values on the left side.

[tex]202 \ cm^{2} =c^{2}[/tex]

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

[tex]\sqrt {202 \ cm^{2} }=\sqrt{c^{2} }[/tex]

[tex]\sqrt {202 \ cm^{2} }=c[/tex]

[tex]14.2126704036 \ cm =c[/tex]

We are told to round to the nearest tenth.

  • 14.2126704036

The 1 in the hundredth place tells us to leave the 2 in the tenth place.

[tex]14.2 \ cm= c[/tex]

The hypotenuse is equal to 14.2 centimeters.

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.