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We know from Pythagoras' Theorem, a right angle triangle can be identified by the relationship:
Thus, we know if the side lengths of the triangle in question abide by this relation, the triangle is right.
First, we must find the greatest side length.
We know, using the distance formula.
From this, we know that:
Therefore, GB would be the hypotenuse of the triangle.
Now we substitute the values for the two shorter lengths and the greater length into the pythagorean theorem:
Therefore, this triangle is a right angled triangle
Thus, we know if the side lengths of the triangle in question abide by this relation, the triangle is right.
First, we must find the greatest side length.
We know, using the distance formula.
From this, we know that:
Therefore, GB would be the hypotenuse of the triangle.
Now we substitute the values for the two shorter lengths and the greater length into the pythagorean theorem:
Therefore, this triangle is a right angled triangle
Question:
Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi27π27, pi cm^3 3 start superscript, 3, end superscript of melted purple liquid. The radius of the cone is 333 cm. What is the height of the cone?
Answer:
The height of the cone is
Explanation:
It is given that the radius of the cone is
The volume of the cone is
The height of the cone can be determine using the formula,
Substituting the values and
, we get,
Multiplying both sides by 3, we have,
Dividing both sides by , we have,
Thus, the height of the cone is