Question

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

Answer 1

Answer is 8√(3)
Solution is given in the picture

Answer 2

hey dear here is ir answer

Let BD is the tree. Because of storm AD is broken and bends as AC.

Here, AC is the broken part of the tree and AB is the part which is still upright.

Here, BC = 8 m, and ∠ BCA=30o

Sum of AB and AC, which is equal to BD shall give the height of the tree.

In Δ ABC;
cosθ=bh=BCACcosθ=bh=BCAC

Or, cos 30°=8ACcos 30°=8AC

Or, √32=8AC32=8AC

Or, AC=(16)(√3)AC=(16)(3)

Now;
tanθ=pb=ABBCtanθ=pb=ABBC

Or, tan 30°=AB8tan 30°=AB8

Or, 1√3=AB813=AB8

Or, AB=8√3AB=83

Height of tree = AB + AC
8√3+16√383+163

=24√3=24√3×√3√3=8√3 m=243=243×33=83 m

Thus, height of the three was 8√3 m