Question

An observer at a distance of 12 cm from a tree looks at the top of the tree, the angle of elevation is 30 degrees. What is the height of the tree. ​

Answer 1

Answer:

4√3 cm

Step-by-step explanation:

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Answer 2

Given :

• Angle of Elevation = 30°

• Distance of the observer from the tree = 12 cm

To find :

The height of the tree.

Solution :

Let the height of the tree be h cm.

Now from the figure, we know that :-

• AB = Height of the triangle
• CB = Base of the triangle
• AC = Hypotenuse of the triangle

Here , we are provided with the base of the triangle.

And we find the height of the tree.

We know that :-

$\bf{tan\:\theta = \dfrac{P}{B}}$

Where :-

• P = Height of the triangle
• B = Base of the triangle

Now by using formula for tan θ , and substituting the values in it , we get :-

$:\implies \bf{tan 30^{\circ} = \dfrac{h}{12}}$

But , we know that $\bf{tan 30^{\circ} = \dfrac{1}{\sqrt{3}}}$ , so Substituting it in the Equation , we get :

$:\implies \bf{\dfrac{1}{\sqrt{3}} = \dfrac{h}{12}}$

By multiplying (12) on both the sides we get :-

$:\implies \bf{\dfrac{1}{\sqrt{3}} \times 12 = \dfrac{h}{12} \times 12}$

$:\implies \bf{\dfrac{12}{\sqrt{3}} = h}$

Now , by multiplying (√3/√3) on both the sides , we get :

$:\implies \bf{\dfrac{12}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} = h \times \dfrac{\sqrt{3}}{\sqrt{3}}}$

$:\implies \bf{\dfrac{12\sqrt{3}}{\sqrt{3} \times \sqrt{3}} = h \times 1}$

$:\implies \bf{\dfrac{12\sqrt{3}}{3} = h}$

$:\implies \bf{4\sqrt{3} = h}$

$\underline{\boxed{\therefore \bf{Height\:(h) = 4\sqrt{3}}}}$

Hence, the height of the tree is 4√3 m.