Question

A vertical tree is growing on the side of a hill with a gradient of 10° to the horizontal. From a point 50m downhill from the tree, the angle of elevation to the top of the tree is 18°. Find the height of the tree. 180 10° -50 m

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Answer 1

Answer:

The answer is - 40 degree

Answer 2

Given:

A vertical tree is growing on the side of a hill with a gradient of 10° to the horizontal. From a point 50m downhill from the tree, the angle of elevation to the top of the tree is 18°

To find: the height of the tree

Explanation:

We have a tree is growing on a hill as given and we have to find the height x of the tree

First for the right angle triangle BCD using trigonometric we can find the unknown lengths BC and BD respectively

   BC = CD × cos (∠ BCS)

         = 50 × cos(10)

         = 50 × 0.9848

         = 49.24m

Now,  for the right angle triangle ABC using trigonometric, we can obtain the length AB as

   AB = BC × tan(18)

         = 49.24 × 0.3249

         = 16m

then, from these we can find the height of the tree xas

    x = AB - AD

       = 16 - 8.68

       = 7.32M