A wheel has radius 30 cm.It rolls along the ground toward a tack that is 58cm from the point where the wheel currently touches the ground. What is the distance between the tack and the closest point on the circumference of the wheel!
I don't understand thus it all! Please help explain how i do this Thank you!!
draw a picture
line from center of circle to tack hits circumference at a right angle (because it is a radius) and therefore that is the closest point to the tack.
also line from circle center to ground is 90 deg
so right triangle
d is hypotenuse center to tack
r^2 + 58^2 = d^2
900 + 3364 = d^2
d = 65.3
subtract radius of 30
35.3 cm
Why did the wheel go to therapy? It had trouble with its "circumference"!
Okay, let's break this down. To find the distance between the tack and the closest point on the circumference of the wheel, we can think of it as a right triangle. The radius of the wheel is one side of the triangle, the distance between the tack and the point of contact is another side, and the distance we're looking for is the hypotenuse.
Using the Pythagorean theorem, we can find the distance by using the formula:
distance^2 = radius^2 + distance between tack and point of contact^2
Plugging in the given values, we get:
distance^2 = 30^2 + 58^2
Solving this equation, we find that the distance is the square root of the sum of the squares of 30 and 58. So grab your calculator, take the square root, and you'll have your answer!
But remember, even if the math gets a little "tacky", don't worry, just keep rolling with it!
To find the distance between the tack and the closest point on the circumference of the wheel, we can draw a line from the tack perpendicular to the ground. This line will intersect the circumference of the wheel at the closest point.
Let's label the point where the wheel touches the ground as A, the tack as T, and the closest point on the wheel's circumference as C.
Since the radius of the wheel is 30 cm, the distance from A to C is 30 cm.
We are given that the distance from T to A is 58 cm. This distance is the hypotenuse of a right triangle with AC as the perpendicular side and TC as the base.
Using the Pythagorean theorem, we can calculate the distance between A and C:
AC^2 + TC^2 = TA^2
Substituting the given values:
30^2 + TC^2 = 58^2
900 + TC^2 = 3364
TC^2 = 3364 - 900
TC^2 = 2464
Taking the square root of both sides:
TC = sqrt(2464)
TC ≈ 49.64 cm
Therefore, the distance between the tack and the closest point on the circumference of the wheel is approximately 49.64 cm.
To find the distance between the tack and the closest point on the circumference of the wheel, we can use the Pythagorean theorem.
Step 1: Draw a diagram to visualize the problem. Label the wheel, the ground, the tack, and the radius.
Step 2: Identify the given information. We are told that the radius of the wheel is 30 cm and the distance from the tack to the point where the wheel touches the ground is 58 cm.
Step 3: Based on the information given, we can form a right triangle. The radius of the wheel is one leg of the triangle, the distance from the tack to the point where the wheel touches the ground is the hypotenuse, and the remaining side is the distance between the tack and the closest point on the circumference of the wheel.
Step 4: Apply the Pythagorean theorem, which 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.
Let's denote the distance between the tack and the closest point on the circumference of the wheel as 'd.' Using the Pythagorean theorem, we have:
d^2 = (58 cm)^2 - (30 cm)^2
d^2 = 3364 cm^2 - 900 cm^2
d^2 = 2464 cm^2
Step 5: Take the square root of both sides of the equation to find the value of 'd.'
d = sqrt(2464 cm^2)
d ≈ 49.6 cm
Therefore, the distance between the tack and the closest point on the circumference of the wheel is approximately 49.6 cm.