Question
ByTo find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. Find the tree tall .
- 144 feet
- 72 feet
- 36 feet
- 48 feet
Hint:
We are given that, mirror is placed on the ground in front of tall pine tree. From the figure, we can see a person standing in front of it. Both the person and the tree forms a triangle with the ground. We are asked to find the height of tree. We will use the properties of the right-angled triangle .
The correct answer is: 72 feet
If we observe the figure, both are forming triangles.
Let the triangle formed by the person be ∆ABC and the triangle formed by the tree be ∆PQR.
From the figure,
AB = 6ft
BC = 2ft
QR = 24ft
Let the height of the tree be “x”.
We have to the height of the tree i.e. side PQ
The ∠ABC and ∠PQR is equal to 90°. As the height of the person and the tree is perpendicular to the ground.
Using the rules of reflection, the incident angle and reflected angle have same value we can write the following equation.
∠ACB = ∠PRQ
So, by AA test both the triangles are similar.
∆ABC ~ ∆PQR
Similar triangles have same shape but different size. Their sides are in proportion to each other. The ratio of their sides is equal.
Using the properties of similar triangle we can find the height of the tree.
We will take the ratios
Therefore, the height of the tree is 72ft.
For such questions, we should know about the properties of similar triangle. We should also know about different tests required to prove the similarity.
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