Questions: Use Pythagorean theorem to find right triangle side lengths Find the value of x in the triangle shown below. Choose 1 answer: (A) x=6 (B) x=8 (C) x=sqrt(15) (D) x=sqrt(34)

Use Pythagorean theorem to find right triangle side lengths

Find the value of x in the triangle shown below.

Choose 1 answer:
(A) x=6
(B) x=8
(C) x=sqrt(15)
(D) x=sqrt(34)

Transcript text: Use Pythagorean theorem to find right triangle side lengths Find the value of $x$ in the triangle shown below. Choose 1 answer: (A) $x=6$ (B) $x=8$ (C) $x=\sqrt{15}$ (D) $x=\sqrt{34}$

Solution

Solution Steps

Step 1: Identify the sides of the right triangle

In the given right triangle, the sides are:

One leg: 3
The other leg: 5
Hypotenuse: $ x $

Step 2: Apply the Pythagorean theorem

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The formula is: \[ a^2 + b^2 = c^2 \] where $ a $ and $ b $ are the legs, and $ c $ is the hypotenuse.

Step 3: Substitute the known values into the formula

Substitute $ a = 3 $, $ b = 5 $, and $ c = x $ into the formula: \[ 3^2 + 5^2 = x^2 \]

Step 4: Calculate the squares of the legs

\[ 3^2 = 9 \] \[ 5^2 = 25 \]

Step 5: Add the squares of the legs

\[ 9 + 25 = 34 \]

Step 6: Solve for $ x $

\[ x^2 = 34 \] \[ x = \sqrt{34} \]