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?

  • A 26.7m
  • B 14.2m
  • C \(1.7+(25\frac{\sqrt{3}}{3}m\)
  • D \(1.7+(25\frac{\sqrt{2}}{2}m\)

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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