a clock has two hands that are 12cm and 15cm in length what is the distance of the tips when the hands are exactly at 2:00?
What’s the answer homie
nvm i finally figured it out !! :D
To find the distance between the tips of the clock hands at 2:00, we can use trigonometry.
First, let's define some variables:
- Length of the shorter hand (hour hand): 12 cm
- Length of the longer hand (minute hand): 15 cm
At 2:00, the hour hand points directly at the number 2 while the minute hand points straight up (towards the number 12).
To use trigonometry, we can consider the angle formed between the hour hand and the vertical line (angle α), as well as the angle formed between the minute hand and the vertical line (angle β).
Since the hour hand points directly at the number 2, which is one-third of the distance between two consecutive hour markers, the angle α can be calculated as follows:
α = (360 degrees / 12 hours) * (2 hours) = 60 degrees
As for the minute hand, it points directly upwards, so the angle β is 0 degrees.
Now, we can calculate the horizontal (x) and vertical (y) components of each hand by using trigonometry.
For the shorter hand:
x = length * cos(α)
x = 12 cm * cos(60 degrees) ≈ 6 cm
y = length * sin(α)
y = 12 cm * sin(60 degrees) ≈ 10.392 cm
For the longer hand:
x = length * cos(β)
x = 15 cm * cos(0 degrees) = 15 cm
y = length * sin(β)
y = 15 cm * sin(0 degrees) = 0 cm
Now, we can calculate the distance (d) between the tips of the clock hands using the Pythagorean theorem.
d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((15 cm - 6 cm)^2 + (0 cm - 10.392 cm)^2)
d ≈ √(81 cm^2 + 107.585664 cm^2)
d ≈ √188.585664 cm^2
d ≈ 13.737 cm
Therefore, the distance between the tips of the clock hands at 2:00 is approximately 13.737 cm.