Q: 55 (NDA-I/2015)
question_subject:
Science
question_exam:
NDA-I
stats:
0,3,5,3,2,3,0
keywords:
{'height': [0, 0, 1, 2], 'tree': [3, 0, 1, 1], 'sun': [3, 0, 0, 6], 'horizon': [0, 0, 1, 5], 'shadow': [2, 1, 0, 1]}
When the sun is 30° above the horizon, we can use the concept of similar triangles to determine the height of the tree. Let`s assume that the height of the tree is h meters.
The shadow of the tree is 17-3 meters long. Since the sun is 30° above the horizon, the shadow, the height of the tree, and the line connecting the top of the tree and the tip of the shadow form a right triangle.
Using trigonometry, we can set up the following equation:
tan(30°) = h / 17-3
Simplifying the equation:
tan(30°) = h / 17-3
1 / sqrt(3) = h / 17.3
After cross-multiplying and simplifying:
h = 17.3 / sqrt(3)
Using a calculator, the approximate value of h is 10 meters.
Therefore, the height of the tree is approximately 10 meters.