When a pendulum swings 35degree from the vertically, the weight moves 15cm horizontally and 5.3 vertically. The length of the pendulum?

sketch the sector to the right of the vertical.

Label the centre as C, the end of the swing as A and the point on the horizontal hitting the pendulum B
So AB = 15 cm
we can find OA
tan 35° = 15/OA
OA = 15/tan35 = 21.422...

so the length of the pendulum is 21.422 + 5.3 = 26.722 cm

To find the length of the pendulum, we can use the concept of proportional triangles and trigonometry. Let's break down the problem step by step:

Step 1: Draw a diagram representing the given scenario.
Draw a vertical line to represent the vertical position of the pendulum, and a horizontal line to represent the horizontal position of the weight. Connect these two lines with a diagonal line, which represents the pendulum's length.

Step 2: Label the relevant measurements.
Label the angle of swing as 35 degrees. Label the horizontal distance moved by the weight as 15 cm and the vertical distance moved as 5.3 cm. Label the length of the pendulum as 'L' (to be determined).

Step 3: Identify the trigonometric relationships.
From the given measurements, we can see that the vertical distance (5.3 cm) corresponds to the adjacent side of the triangle, while the horizontal distance (15 cm) corresponds to the opposite side. The angle of swing (35 degrees) corresponds to the angle between the hypotenuse (pendulum length) and the adjacent side.

Step 4: Use trigonometry to solve for the length of the pendulum.
In the right triangle, we can use the tangent function to relate the angle, opposite side, and adjacent side:
tan(angle) = opposite / adjacent

Plugging in the values we know:
tan(35 degrees) = 5.3 cm / 15 cm

Now, we can rearrange the equation to solve for the pendulum length, L:
L = opposite / tan(angle)
L = 5.3 cm / tan(35 degrees)

Using a calculator, we can find the approximate value of the tangent of 35 degrees to be 0.7002. Therefore:
L = 5.3 cm / 0.7002
L ≈ 7.571 cm

Hence, the length of the pendulum is approximately 7.571 cm.