The picture below shows a pole and its shadow:
A pole is shown with a right triangle side. The right triangle has hypotenuse 365 cm and base 27 cm.
What is the height of the pole? (1 point)
196 centimeters
244 centimeters
338 centimeters
364 centimeters
To find the height of the pole, we can use the Pythagorean theorem. The formula for the Pythagorean theorem is a^2 + b^2 = c^2, where a and b are the legs of the right triangle, and c is the hypotenuse.
In this case, the base of the triangle is 27 cm, and the hypotenuse is 365 cm. We can let the height of the pole, which is the other leg of the triangle, be represented by variable h.
Using the Pythagorean theorem, we have 27^2 + h^2 = 365^2. Simplifying this equation gives us h^2 = 365^2 - 27^2.
Calculating:
h^2 = 133225 - 729
h^2 = 132496
h = √132496
h ≈ 364
Therefore, the height of the pole is approximately 364 centimeters.