Question

1. In a right triangle, the lengths of the legs are a and b. Find the length of a hypotenuse, if: a=1, b=1; 2. In a right triangle, the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg, if: c=5, a=3;

Answer 1

1.
`c = √(2)`.

2. b = 4.

Explanation:

To solve these two questions, keep the Pythagorean Theorem in mind:
`a^2 + b^2 = c^2`. Also remember that measurements cannot be negative, so we will disregard the negative answers.

1. a = 1, and b = 1. c = ?

`1^2 + 1^2 = c^2`

`1 + 1 = c^2\\`

`c^2 = 1 + 1\\c^2 = 2\\√(c^2) = √(2)\\c = √(2)`

2. a = 3, c = 5. b = ?

`3^2 + b^2 = 5^2\\9 + b^2 = 25\\b^2 = 16\\√(b^2) = √(16)\\b = 4`

Hope this helps!