The Pythagorean Theorem can be used to find the missing side length of a triangle when two other side lengths are known.
Consider the following measurements.
a=20
b=?
c=29
Use the formula c=a2+b2−−−−−−√, a modified version of the Pythagorean Theorem, to find the missing side length, b.
What is the value of b?
A) 441
B) 840.8
C) 35.2
D) 21
C) 35.2
To find the missing side length, b, we can use the modified version of the Pythagorean Theorem, which states c = √(a^2 + b^2).
In this case, we have:
a = 20
c = 29
Substituting these values into the formula c = √(a^2 + b^2), we get:
29 = √(20^2 + b^2)
To isolate b^2, we can square both sides of the equation:
29^2 = (20^2 + b^2)^2
841 = 400 + b^2
Subtracting 400 from both sides of the equation, we have:
441 = b^2
To find the value of b, we take the square root of both sides:
b = √441
b = 21
Therefore, the value of b is D) 21.
To find the missing side length, b, using the Pythagorean Theorem, we can rearrange the formula as follows:
b = √(c^2 - a^2)
Given that a = 20 and c = 29, we can substitute these values into the formula:
b = √(29^2 - 20^2)
Calculating this expression:
b = √(841 - 400)
b = √441
Therefore, the value of b is the square root of 441, which is 21.
So, the correct answer is:
D) 21