A man 1.7m tall observes a bird on top of a tree at an angle of 30°. if the distance between the man's head and the bird is 25m, what is the height of the tree?
The correct answer is B. 14.2m
Sure! Let's say the height of the tree is h meters. The distance between the man's head and the bird is 25m, and the angle between them is 30°. We can use trigonometry to find the height of the tree.
The distance between the man's head and the bird is the hypotenuse of a right triangle, where the height of the tree is the side opposite to the 30° angle. Using the sine function, we have:
\(\sin(30°) = \frac{\text{opposite}}{\text{hypotenuse}}\)
\(\sin(30°) = \frac{h - 1.7}{25}\)
Substituting the value of \(\sin(30°) = 0.5\), we get:
\(0.5 = \frac{h - 1.7}{25}\)
Multiplying both sides by 25, we get:
12.5 = h - 1.7
Adding 1.7 to both sides, we get:
h = 14.2
So, the height of the tree is 14.2m.
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