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Any Point Equidistant from the End Points of a Segment Lies on the Perpendicular Bisector of the Segment

Consider a tr...

Question

Consider a triangular plot $A B C$ with sides $A B = 7 m$ , $B C = 5 m$ and $C A = 6 m$ . A vertical lamp-post at the mid point $D$ of $A C$ subtends an angle $30^{o}$ . The height $(i n m)$ of the lamp-post is?

7 \sqrt{3}

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\frac{2}{3} \sqrt{21}

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\frac{3}{2} \sqrt{21}

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2 \sqrt{21}

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Solution

The correct option is B $\frac{2}{3} \sqrt{21}$
BD $= h cot 30^{o} = h \sqrt{3}$

So, $7^{2} + 5^{2} = 2 (h \sqrt{3})^{2} + 3^{2})$

$\Rightarrow 37 = 3 h^{2} + 9$ .

$\Rightarrow 3 h^{2} = 28$

$\Rightarrow h = \sqrt{\frac{28}{3}} = \frac{2}{3} \sqrt{21}$ .

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Consider a triangular plot ABC with sides AB=7 m, BC=5 m and CA=6 m. A vertical lamp-post at the mid point D of AC subtends an angle 30o. The height (in m) of the lamp-post is?

The correct option is B 23√21BD=hcot30o=h√3So, 72+52=2(h√3)2+32)⇒37=3h2+9.⇒3h2=28⇒h=√283=23√21.

Consider a triangular plot $A B C$ with sides $A B = 7 m$ , $B C = 5 m$ and $C A = 6 m$ . A vertical lamp-post at the mid point $D$ of $A C$ subtends an angle $30^{o}$ . The height $(i n m)$ of the lamp-post is?

The correct option is B $\frac{2}{3} \sqrt{21}$
BD $= h cot 30^{o} = h \sqrt{3}$

So, $7^{2} + 5^{2} = 2 (h \sqrt{3})^{2} + 3^{2})$

$\Rightarrow 37 = 3 h^{2} + 9$ .

$\Rightarrow 3 h^{2} = 28$

$\Rightarrow h = \sqrt{\frac{28}{3}} = \frac{2}{3} \sqrt{21}$ .