What is the length of the shadow cast on the vertical screen by your 10.0 cm hand if it is held at an angle of θ=30.0∘ above horizontal?

Length of shadow cast by hand = 5.0 cm

Explanation:

With the hand inclined at an angle θ=30.0∘ above horizontal, it can be imagined to form part of a right angled triangle that has the following parts

vertical screen=vertical part of the triangle where we cast the shadow of the hand

The hand=the hypotenuse side

The horizontal = side to which the hand makes the 30.0° angle

By trigonometric relationship

Sin θ° = Opposite/hypotenuse

Sin θ° = (Shadow cast by hand) / (Length of hand)

Sin 30° = (length of shadow cast by hand) / 10cm

or 0.5 = (length of shadow cast by hand) / 10cm

Length of shadow cast by hand = 0.5 * 10cm = 5.0 cm