Question

to get from your house to class you walk east 579 feet. after class you walk south west 965 feet to meet your friends at lunch. when walking north the 772 feet back home from lunch, what type of triangle did you form?
a. none
b. acute triangle
c. right triangle
d. obtuse triangle
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Recall the triangle type rules

To determine the triangle type, we use the Pythagorean theorem and its extensions. For a triangle with side lengths \(a\), \(b\), \(c\) (where \(c\) is the longest side):

• If \(a^{2}+b^{2}=c^{2}\), it's a right triangle.
• If \(a^{2}+b^{2}>c^{2}\), it's an acute triangle.
• If \(a^{2}+b^{2}

Step2: Identify the sides

Let \(a = 579\), \(b = 772\), \(c = 965\) (since 965 is the longest side).

Step3: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

• \(a^{2}=579^{2}=579\times579 = 335241\)
• \(b^{2}=772^{2}=772\times772 = 595984\)
• \(a^{2}+b^{2}=335241 + 595984=931225\)
• \(c^{2}=965^{2}=965\times965 = 931225\)

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(a^{2}+b^{2}=c^{2}\) (both equal to 931225), the triangle satisfies the Pythagorean theorem for a right triangle.

Answer:

C. right triangle