8. The topmost branch of a tree is tied with a string attached to a pole in the ground. The length of this string is $200m$ and it makes an angle of ${{45}^{\circ }}$with the ground. Find the distance of the pole to which the string is tied from the base of the tree.

Home » 8. The topmost branch of a tree is tied with a string attached to a pole in the ground. The length of this string is and it makes an angle of with the ground. Find the distance of the pole to which the string is tied from the base of the tree.

8. The topmost branch of a tree is tied with a string attached to a pole in the ground. The length of this string is $200m$ and it makes an angle of ${{45}^{\circ }}$ with the ground. Find the distance of the pole to which the string is tied from the base of the tree.

Class 10 | Frank | Heights and Distances | ICSE | Maths

8. The topmost branch of a tree is tied with a string attached to a pole in the ground. The length of this string is $200m$ and it makes an angle of ${{45}^{\circ }}$ with the ground. Find the distance of the pole to which the string is tied from the base of the tree.

According to the question,

Let us assume that the topmost branch of the tree is Q and the pole on the ground to which the topmost branch is tied is R

In ΔPQR,

$\cos {{45}^{\circ }}=\frac{PR}{PQ}$

$\frac{1}{\sqrt{2}}=\frac{h}{200}$

$h=\frac{200}{\sqrt{2}}$

$h=\frac{200}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

$h=100\sqrt{2}$

$h=100\times 1.41$

$h=141.4m$ Therefore, the required distance between the pole to which the string is tied and the base of the tree $141.4m$

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