Question

mp persevere with problems the radius of the circle shown is 4 centimeters. one of the legs of the right triangle formed is also 4 centimeters. find the length of leg x. round to the nearest tenth.

Explanation:

Step1: Identify the hypotenuse

The hypotenuse of the right triangle is the diameter of the circle. Since the radius is 4 cm, the diameter is \( 2\times4 = 8 \) cm.

Step2: Apply the Pythagorean theorem

Let the two legs be \( a = 4 \) cm, \( x \), and hypotenuse \( c = 8 \) cm. The Pythagorean theorem is \( a^2 + x^2 = c^2 \). Substitute the known values: \( 4^2 + x^2 = 8^2 \).

Step3: Solve for \( x \)

First, calculate \( 4^2 = 16 \) and \( 8^2 = 64 \). Then the equation becomes \( 16 + x^2 = 64 \). Subtract 16 from both sides: \( x^2 = 64 - 16 = 48 \). Take the square root: \( x = \sqrt{48} \approx 6.9 \) (rounded to the nearest tenth).

Answer:

\( 6.9 \) centimeters