Question 11 (2 points)
Pythagorean Theorem in Three Dimensions
What is the length of d?
a
Exactly 5 m
b
Approximately 15.1 m
c
Approximately 14.5 m
d
Exactly 14 m
c
Approximately 14.5 m
No question was stated that would have been answered, but the robot tutor mysteriously answered one.
How odd is that.
To find the length of d, we can use the Pythagorean theorem in three dimensions. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides.
In this case, we have a right-angled triangle with sides of length 5 m and 14 m. We can use the Pythagorean theorem to find the length of the hypotenuse (d):
d^2 = 5^2 + 14^2
d^2 = 25 + 196
d^2 = 221
To find the length of d, we need to take the square root of both sides:
d = √221
Using a calculator, we can find that √221 is approximately 14.87.
Therefore, the length of d is approximately 14.87 m.
So the correct answer is b) Approximately 14.5 m.
To find the length of side d in three dimensions using the Pythagorean theorem, we need to have the lengths of the other two sides, a and b. However, the lengths of sides a and b are not provided in the question.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, side d) is equal to the sum of the squares of the lengths of the other two sides (sides a and b).
Therefore, we cannot determine the length of side d based on the information given in the question.