Question

2. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.



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Answer 1

Answer:

Draw a figure. Let AC be the broken part of the tree. Angle C = 30°

BC = 8 m

To Find:

Height of the tree, which is ABIn right ΔABC,

Using Cosine and tangent angles,

cos 30° = BC/AC

We know that, cos 30° = √3/2

√3/2 = 8/AC

AC = 16/√3 …(1)

Also,

tan 30° = AB/BC

1/√3 = AB/8

AB = 8/√3 ….(2)

Therefore, total height of the tree = AB + AC = 16/√3 + 8/√3 = 24/√3 = 8√3 m.

hope this helps you

Answer 2

Let the Height of the Tree =AB+AD

and given that BD=8 m

Now, when it breaks a part of it will remain perpendicular to the ground (AB) and remaining part (AD) will make an angle of 30 Degree

Now, in △ABD

cos30 Degree = $\frac{BD}{AD}$ = BD = $\frac{√3AD}{2}$

= AD = $\frac{2×8}{√3}$

also, in the same Triangle

tan30 Degree = $\frac{AB}{BD}$ = AB = $\frac{8}{√3}$

∴ Height of tree = AB + AD =

$\frac{16}{√3}$ + $\frac{8}{√3}$ metre =

$\frac{24}{√3}$ metre = 8√3 metre