The upper part of a tree broken over by the wind makes an angle of 30 o with the ground, and the distance from the root to the point where the top of the tree touches the ground is 15 m. Using sine rule, find the height of the tree.

Question

Philoid · Accepted Answer

Let BD be the tree, let A be the point where the tree is broken by the wind.

And according to the given condition,

AD = AC

Now let AB = x and AC = y = AD

So the total height of the tree is AB + AD = x + y

Now in ΔABC,

∠C = 30°, ∠B = 90°,

So, ∠A = 180° - (∠B + ∠C) (∵ π = A + B + C)

Hence ∠A = 180° - (90° + 30°) = 60°

Now applying sine rule, we get

Now substituting the values obtained, we get

Substituting the corresponding values, we get

So,

And also from (i),

⇒y = 10√3 m

So the height of the tree is

x + y = 5√3 + 10√3 = 15√3 m

The upper part of a tree broken over by the wind makes an angle of 30o with the ground, and the distance from the root to the point where the top of the tree touches the ground is 15 m. Using sine rule, find the height of the tree.

The upper part of a tree broken over by the wind makes an angle of 30^o with the ground, and the distance from the root to the point where the top of the tree touches the ground is 15 m. Using sine rule, find the height of the tree.