The picture below shows a pole and its shadow:
A pole is shown with a right triangle side. The right triangle has hypotenuse 113 cm and base 15 cm.
What is the height of the pole? (1 point)
112 centimeters
100 centimeters
98 centimeters
64 centimeters
To find the height of the pole, we need to find the length of the side opposite to the angle between the hypotenuse and the base of the triangle. This can be found using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, the hypotenuse is 113 cm (c) and the base is 15 cm (a). Let's call the height of the pole (b).
Using the Pythagorean theorem:
c^2 = a^2 + b^2
113^2 = 15^2 + b^2
12769 = 225 + b^2
b^2 = 12544
Taking the square root of both sides:
b = √12544
b ≈ 112 cm
Therefore, the height of the pole is approximately 112 centimeters.