Need help with this trigonometry word problem From the top of the tower 30 m height a man is observing the base of a tree at an angle of depression measuring 30 degree. Find the distance between the tree and the tower.
Please show your work

The distance between the tree and the tower is 30√3m.

Justification:

Let the situation be in a right angleABC form as shown in attached figure.

Given the height of the tower is 30m and the angle of depression to the base of the tree measure 30°.

So, In ΔABC

tanθ = p/b

tan30° = 30/BC

1/√3 = 30/BC

BC = 30√3m.

  30√3 m ≈ 52 m

Step-by-step explanation:

The side ratios in a 30°-60°-90° triangle are 1 : √3 : 2. The long leg of the triangle is √3 times 30 m, or about 51.96 m.

The distance between the tree and the tower is about 30√3 m ≈ 52 m.

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If you haven't memorized the ratios of this special triangle, you can use the relation ...

  Tan = Opposite/Adjacent

  tan(30°) = 30/d

  d = 30/tan(30°) = 30√3 = 51.96 . . . . same as above