Question

a tree is broken without separating from the stem by the wind the top touches the ground making an angle 30 degrees at a distance of 12cm from the foot of the tree find the hieght of tree before breaking​

Answer 1

Step-by-step explanation:

√12=x^2+x^2. let's take therefore x=√6

Answer 2

Given,

A tree is broken without separating from the stem by the wind.

The top touches the ground making an angle 30°, at a distance of 12 cm, from the foot of the tree.

To find,

The height of the tree before breaking.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the length of the upper broken of the tree is x cm, and the length of the unbroken lower part is y cm, respectively.

Now, according to the question;

The upper broken part of the tree forms the hypotenuse of an imaginary right-angled triangle whole perpendicular is represented by the height of the lower unbroken part of the tree and the base is represented by the horizontal distance between the tip of the tree and the base of the tree. The acute angle opposite to the perpendicular is 30°.

Now,

As per trigonometry, on applying the Tan and Cos ratio formula for the given angle, we get;

Tan 30° = (perpendicular)/(base)

=> 1/√3 = (y cm)/(12 cm)

=> y = 12/√3 cm = 4√3 cm

=> length of the unbroken lower part = 4√3 cm

And, Cos 30° = (base)/(hypotenuse)

=> √3/2 = (12 cm)/(x cm)

=> x = 24/√3 cm = 8√3 cm

=> length of the upper broken of the tree = 8√3 cm

So, the height of the tree before breaking

= (length of the unbroken lower part) + (length of the upper broken of the tree)

= 4√3 cm + 8√3 cm

= 12√3 cm

Hence, the height of the tree, before breaking, is equal to 12√3 cm.