Solve the problem. Type the number in the box that correctly completes the sentence.Nimrod wanted to build a tower three miles high. He wants to know how far would it be from the top of his tower to a point four miles away from the base of the tower. The distance would be Answer
miles.
Answers
Answer:
5 miles
Step-by-step explanation:
Think of this like a triangle. From the bottom of the tower, to the top of the tower, to the point 3 miles away, and back to the bottom of the tower.
So we already have 2 side lengths. The height of the tower, 3 miles, and the base, 4 miles. In order to find the 3rd length, the distance from the top of the tower to the point 4 miles away from the bottom, we need to apply the formula A squared + B squared = C squared.
We have A and B, (3 and 4) and we need C.
A squared (3 squared) is 9
B squared (4 squared) is 16
so 9 + 16 = C squared
9 + 16 = 25
C squared = 25
square root of 25 is 5
C = 5
The distance from the top of the tower to the point 4 miles away is 5.
Final answer:
By applying the Pythagorean theorem to the given problem, we find that the distance from the top of the tower to the point four miles away from the base of the tower is 5 miles.
Explanation:
Nimrod's problem is a classic application of the Pythagorean Theorem, which 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 other two sides. In this case, the height of the tower is one side of the triangle (3 miles), and the distance from the base of the tower to the point Nimrod is interested in is the other side (4 miles). The distance from the top of the tower to that point is the hypotenuse.
Applying the Pythagorean theorem, we have: (Height of the tower)² + (Distance from the base to the point)² = (Distance from the top to the point)². So, this becomes: 3² + 4² = (Distance from the top to the point)². That simplifies into 9 + 16 = (Distance from the top to the point)², or 25 = (Distance from the top to the point)².
To find the actual distance (the length of the hypotenuse), we take the square root of 25, which is 5. Therefore, the distance from the top of the tower to the point four miles away from the base is 5 miles.
Using the Pythagorean theorem (a² + b² = c²), we can find the hypotenuse:
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²
c = √25
c = 5
So the distance from the top of the tower to the point four miles away from the base is 5 miles.
Learn more about Pythagorean theorem here:
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A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
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The expression a single Trigonometric function
Let's express the expression in terms of a single trigonometric function or a power of a trigonometric function, we can simplify it as follows:
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Answer:
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