Question

A student stands 20 m away from the foot

of a tree and observes that the angle of elevation of the top of the tree, measured from a table 1.5 m above the ground, is 34°28'. Calculate the height of the tree to
the nearest metre.
​

Answer 1

15 m

Explanation:

the other guy has explained it well enough

Answer 2

Height of tree is
`\approx` 15 m.

Explanation:

Given that student is 20 m away from the foot of tree.

and table is 1.5 m above the ground.

The angle of elevation is: 34°28'

Please refer to the attached image. The given situation can be mapped to a right angled triangle as shown in the image.

AB = CP = 20 m

CA = PB = 1.5 m

`\angle C` = 34°28' = 34.46°

To find TB = ?

we can use trigonometric function tangent to find TP in right angled
`\triangle TPC`

`tan \theta = (Perpendicular)/(Base)\\tan C= (PT)/(PC)\\\Rightarrow tan 34.46^\circ = (PT)/(20)\\\Rightarrow PT = 20 * 0.686 \\\Rightarrow PT = 13.72\ m`

Now, adding PB to TP will give us the height of tree, TB

Now, height of tree TB = TP + PB

TB = 13.72 + 1.5 = 15.22
`\approx` 15 m