Question

While you’re at the top of the tower (50 meters up), you see an ant walking along the edge of the building. If the ant were to walk straight down the side of the tower (86-degree lean) until it reaches the ground, how far would the ant travel? Which trigonometric ratio would you use? Use the ratio to find the measurement. Confirm that answer by using the Pythagorean theorem instead of trig ratios.

a) Tan
b) Cos
c) Sin
d) Sec

Answer 1

To find the distance the ant would travel if it walked straight down the side of the tower, use the sine (sin) trigonometric ratio. Confirm the answer by using the Pythagorean theorem.

Step-by-step explanation:

To find the distance the ant would travel if it walked straight down the side of the tower, we can use trigonometry. The trigonometric ratio we would use in this case is sine (sin). The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. In this case, the length of the side opposite the angle is 50 meters (the height of the tower) and the length of the hypotenuse is the distance the ant would travel. Therefore, using sin(86 degrees) = 50/hypotenuse, we can solve for the hypotenuse.

Once we find the length of the hypotenuse using trigonometry, we can confirm our answer by using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the lengths of the other two sides are 50 meters and the distance the ant would travel. By using the Pythagorean theorem, we can verify that our answer is correct.