Question

Lots of points! The information given represents lengths of sides of a right triangle with c the hypotenuse. Find the correct missing length to the nearest hundredth. A calculator may be helpful.

a = 16, b = 28, c = ___

Which of the following answer choices would fit in the blank space?

A. 31.46

B. 31.94

C. 32.09

D. 32.25

Explain your answer please, don't just put one of the choices and leave! ;)

Answer 1

Hey there.

To solve this problem we have to use the Pythagorean theorem. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate c² we have to do α² + β² = c².

Given

⇒ a² = 16

⇒ b² = 28

⇒ c² = unknown

To solve the problem you have to add a² and b².

a² = 16
b² = 28

16² + 28² = c²

16² = 16 x 16
28² = 28 x 28

16² = 256
28² = 784

258 + 784 = 1040

a² + b² = 1040

The next step is to find the square root of 1040

√1042 = 32.2490


= 32.2490 is rounded to 32.25

Answer = (D)

Answer 2

Pythagoras Theorem:
hipotenuse²=side1² +side2²

a=is the longest side of the triangle (hypotenuse)
b and c: are the other two sides.

In this case:
hipotenuse²=side₁² + side₂²

side₁=a=16
side₂=b=28

c²=16²+28²
c²=256+784
c²=1040
c=√1040=32.2490....≈32.25

Answer: D. 32.25