easy

Pythagorean Theorem Problems - easy

Problem №1

Could a right triangle have sides: 3, 4, 5?
Answers: yes or no.

Solution:
3² + 4² = 5²
because 25=25 so a right triangle can have sides 3, 4, 5

Problem №2

Given a right triangle ABC, $\angle C = 90 ^{\circ}$ , in which AC=3, BC=4. Determine the length of AB.

Solution:
By the Pythagorean theorem we have: $AB^2=AC^2+BC^2=3^2+4^2=9+16=25$ . Since $AB^2=5^2$ , AB=5.

Problem №3

Given a right triangle ABC, $\angle C = 90 ^{\circ}$ , in which AC=7, BC=24. Determine the length of AB.

Solution:
By the Pythagorean theorem we have: $AB^2=AC^2+BC^2=7^2+24^2=49+576=625$ . Since $AB^2=25^2$ , AB=25.

Problem №4

Given a right triangle ABC, $\angle C = 90 ^{\circ}$ , in which AC=8, BC=15. Determine the length of AB.

Solution:
By the Pythagorean theorem we have: $AB^2=AC^2+BC^2=8^2+15^2=64+225=289$ . Since $AB^2=17^2$ , AB=17.