You visited us 1 times! Enjoying our articles? Unlock Full Access!

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}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 \sqrt{21}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

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

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

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

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

Suggest Corrections

Similar questions

Q. 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

A C

subtends an angle

30^{\circ}

B

. The height (in

m

) of the lamp-post is :

Q. Consider a triangle 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

A C

subtends an angle

30^{o}

B

. The height

(i n m)

of the lamp post is:

Q. 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

A C

subtends an angle

30^{\circ}

B

. The height (in

m

) of the lamp-post is :

Q. Consider a triangular plot ABC with sides AB = 7 m, BC = 5 m and CA = 6 m. A vertical lamp-post at the midpoint D of AC subtends an angle

30^{\circ}

at B. The height (in m) of the lamp-post is:

Q. A lamp post is situated at the middle point

M

of the side

A C

of a triangular plot

A B C

with

B C = 7 m, C A = 8 c m

and

A B = 9 m

. Lamp post subtends angle

15^{o}

at the point

B

. Determine the height of the lamp post.

Join BYJU'S Learning Program

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

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

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

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