In a right triangle, how do you find the exact value of c if a=14 b=14?

Question

In a right triangle, how do you find the exact value of c if a=14  b=14?

HIX Tutor · Accepted Answer

undefined To find the exact value of the hypotenuse (c) in a right triangle, you can use the Pythagorean theorem, which says: c^2 = a^2 + b^2.
1. Substitute the values of a and b into the formula: c^2 = 14^2 + 14^2.
2. Simplify the equation: c^2 = 196 + 196.
3. Add the numbers: c^2 = 392.
4. Take the square root of both sides to find c: c = √392.
5. Simplify the square root: c = 14√2.
Therefore, the exact value of c is 14√2.

Carter Anderson · Answer

The hypotenuse is exactly #14sqrt 2#.

This is an iscoseles right triangle in which the angles are 45-45-90. Sides a and b are equal, and the hypotenuse,c, is the length of one side times #sqrt 2#. Since both sides a and b are 14, the hypotenuse, c, is #14sqrt 2#.

Charles Autterson · Answer

undefined In a right triangle, you can find the exact value of the hypotenuse $ c $ using the Pythagorean theorem, which states:

$$ c^2 = a^2 + b^2 $$

Given $ a = 14 $ and $ b = 14 $, you substitute these values into the formula:

$$ c^2 = 14^2 + 14^2 $$
$$ c^2 = 196 + 196 $$
$$ c^2 = 392 $$

To find $ c $, you take the square root of both sides:

$$ c = \sqrt{392} $$

Thus, the exact value of $ c $ is $ \sqrt{392} $.