HELP ME WITH THIS QUESTION

Question

Three people are sitting on a bus. Vivian is directly behind Ariel and directly left of Ron. If Ariel and Vivian are 7 feet apart, and Ron and Ariel are 10 feet apart, what is the distance between Vivian and Ron? If necessary, round to the nearest tenth.

Answer 1

Sketch a diagram to help you visualize it if you need to.

Since Vivian is behind Ariel and to the left of Ron, she is at the 90 degree angle of a right triangle.

The distance between Vivian and Ariel (7 ft) is one leg of the triangle.

The distance between Ron and Ariel (10 ft) is the hypotenuse.

Use the Pythagorean theorem to find the length of the other leg.

A and B are legs, H is the hypotenuse:

Pythagorean theorem is: H² = A² + B²

But we need one of the legs, so let's solve this for B

B² = A² - H²

B=sqrt(A² - H²)

B = sqrt(10² - 7²) = sqrt(100-49) = sqrt(51) = 7.1ft