Question

he height of two trees are 6m and 12m. their bases are 8m apart. find the distance between the top most points of the tree. plz do this i will mark them as brainlest. please also do the working so that i can understand better.

Answer 1

${\underline{\underline{\bf{Given:}}}}$

• The heights is two trees are 6 m and 12 m.
• The distance between their bases is 8 m.

${\underline{\underline{\bf{Need\:to\: find:}}}}$

• The distance between the top points of both the trees.

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

Pythagorean Theorem:

$\:\:\:\:\:\:\:\:\:\:\underline{\boxed{\sf{{a}^{2}+{b}^{2}={c}^{2}}}}$

${\underline{\underline{\bf{Solution:}}}}$

Let's assume that the top of tree joins (dotted lines) from tree-A to tree-B, it forms a right-angled triangle. We are also given with the measures. So, we can find the answer by using Pythagorean Theorem. It's hypotenuse equals the distance between their top points.

$\:\:\:\:\:\:\sf{a=6\:m\:(Length\:of\:Tree\:B - length\:of\:Tree\:A)}$

$\:\:\:\:\:\:\sf{b=8\:m\:(Distance\: between\:the\:base)}$

$\:\:\:\:\:\:\sf{c=Hypotenuse\:(?)}$

Now, by putting the measures in the formula,

$\:\:\:\:\:\:\implies{\sf{{a}^{2}+{b}^{2}={c}^{2}}}$

$\:\:\:\:\:\:\implies{\sf{{6}^{2}+{8}^{2}={c}^{2}}}$

$\:\:\:\:\:\:\implies{\sf{36+64={c}^{2}}}$

$\:\:\:\:\:\:\implies{\sf{100={c}^{2}}}$

$\:\:\:\:\:\:\implies{\sf{\sqrt{100}=c}}$

$\:\:\:\:\:\:\implies{\sf{\red{\underline{\underline{10\:m=c}}}}}$

${\underline{\underline{\bf{Required\:answer:}}}}$

• The distance between the top points of Tree-A and Tree-B is 10 cm.

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