When the sun is 30 above the horizon, shadow of one tree is 17-3 m long. What is the height of this tree ?

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Q: 55 (NDA-I/2015)
When the sun is 30° above the horizon, shadow of one tree is 17-3 m long. What is the height of this tree ?

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.