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?
Draw a diagram It should be clear that
h/10 = sin30°
assuming the light shines horizontally.
To find the length of the shadow cast on the vertical screen by your hand, you can use trigonometry. In this case, we can use the tangent function.
The tangent of the angle θ can be defined as the ratio of the length of the opposite side to the length of the adjacent side. In this scenario, the hand becomes the adjacent side and the shadow length becomes the opposite side.
Let's break down the information given:
- Hand length (adjacent side): 10.0 cm
- Angle θ: 30.0∘
To find the length of the shadow, we can use the tangent function:
tan(θ) = opposite / adjacent
tan(30.0∘) = shadow length / 10.0 cm
Now we can solve for the shadow length:
shadow length = tan(30.0∘) * 10.0 cm
To find the value of tan(30.0∘), you can use a calculator or reference a trigonometric table. The tangent of 30.0∘ is approximately 0.5774.
shadow length = 0.5774 * 10.0 cm
shadow length ≈ 5.77 cm
Therefore, the length of the shadow cast on the vertical screen by your 10.0 cm hand, when held at an angle of 30.0∘ above horizontal, is approximately 5.77 cm.