When the angle of elevation of the sun is 45°, the shadow of a coconut tree is 18 meters in length. What is the height of the coconut tree? (Your answer will be a whole numerical value only.)
Question
When the angle of elevation of the sun is 45°, the shadow of a coconut tree is 18 meters in length. What is the height of the coconut tree? (Your answer will be a whole numerical value only.)
Solution 1
To solve this problem, we can use the properties of a 45°-45°-90° triangle. In such a triangle, the lengths of the two legs are equal.
Here, the angle of elevation of the sun is 45°, which means the angle between the coconut tree (which we can consider as a vertical line) and its shadow (which we can consider as a horizontal line) is also 45°.
So, the height of the coconut tree is equal to the length of its shadow.
Therefore, the height of the coconut tree is 18 meters.
Solution 2
To solve this problem, we can use the properties of a 45°-45°-90° triangle. In such a triangle, the lengths of the two legs are equal.
Here, the angle of elevation of the sun is 45°, which means the angle between the coconut tree (which we can consider as one leg of the triangle) and its shadow (which we can consider as the other leg of the triangle) is also 45°.
Since the length of the shadow is given as 18 meters, the height of the coconut tree will also be 18 meters.
So, the height of the coconut tree is 18 meters.
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