Question

2
32 which of the following correctly uses the pythagorean theorem to find the missing side x ?
image of right triangle with hypotenuse 10, one leg 8, and the other leg x
a ( 8^2 + (10)^2 = x^2 )
b ( x + 8 = 10 )
c ( x^2 + 8^2 = (10)^2 )
d ( x^2 + (10)^2 = 8^2 )
33 what is the length of the unknown side?
image of right triangle with one leg 16, one leg 12, and hypotenuse x
a 14 units
b 20 units
c 28 units
d 200 units

Explanation:

Question 32

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem states that for a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse (the side opposite the right angle) and \( a, b \) are the legs (the other two sides). In the given triangle, the hypotenuse is 10, and the legs are 8 and \( x \).

Step2: Apply the Theorem

So, substituting into the formula, we get \( x^2 + 8^2 = 10^2 \), which matches option C.

Step1: Identify Sides

In the right triangle, the legs are 16 and 12, and \( x \) is the hypotenuse.

Step2: Apply Pythagorean Theorem

Using \( a^2 + b^2 = c^2 \), we have \( 16^2 + 12^2 = x^2 \).

Step3: Calculate Squares

\( 16^2 = 256 \) and \( 12^2 = 144 \).

Step4: Sum the Squares

\( 256 + 144 = 400 \).

Step5: Take Square Root

\( x = \sqrt{400} = 20 \).

Answer:

C. \( x^2 + 8^2 = (10)^2 \)

Question 33