The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the...

The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number.

Answer Details

To solve this problem, we can use basic trigonometry.

Let's draw a diagram to visualize the problem:

           * 
         / | \
        /  |  \
     h /   |   \ 60m
      /    |    \
     /     |78° \
    *------x------*
         60m

In the diagram, the tree is represented by a point at the top, the point on the ground where the angle of elevation is measured is represented by "x", and the height of the tree is represented by "h".

We know that the angle of elevation from point "x" to the top of the tree is 78°. Therefore, the angle between the horizontal and the line from point "x" to the top of the tree is also 78°.

Using trigonometry, we can find the height of the tree "h" by using the tangent function:

tan(78°) = h/60m

To solve for "h", we can multiply both sides by 60m:

h = 60m * tan(78°)

Using a calculator, we can find that:

h ≈ 282.79m

Therefore, the height of the tree is approximately 282m (rounded to the nearest whole number).

So, the correct answer is:

282m.