MyQuestionIcon

1

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

Area of a Triangle

A lamp post i...

Question

A lamp post is situated at the middle point m of the side ac of a triangular plot ABC with BC=7CM, CA=8M and AB=9M. Lamp posts subtend an $∠ 15^{\circ}$ at the point B.determine the height of the lamp post.

Open in App

Solution

To prove: $t a n (\frac{B - C}{2}) = (\frac{b - c}{b + c}) c o t \frac{A}{2}$
Then, a = k sin A, b = k sin B, c = k sin C
$R . H . S = (\frac{b - c}{b + c}) c o t \frac{A}{2}$
$= (\frac{k s i n B - k s i n C}{k s i n B + k s i n C}) c o t \frac{A}{2}$
$= (\frac{s i n B - s i n C}{s i n B + s i n C}) c o t \frac{A}{2}$
$= [\frac{2 s i n (\frac{B - C}{2}) c o s (\frac{B + C}{2})}{2 s i n (\frac{B + C}{2}) c o s (\frac{B - C}{2})}] c o t \frac{A}{2}$
$= t a n (\frac{B - C}{2}) c o t (\frac{B + C}{2}) c o t \frac{A}{2}$
$= t a n (\frac{B - C}{2}) c o t (\frac{π}{2} - \frac{A}{2}) c o t \frac{A}{2}$
$= t a n (\frac{B - C}{2}) t a n \frac{A}{2} c o t \frac{A}{2}$
$= t a n (\frac{B - C}{2})$
= L.H.S

Suggest Corrections

thumbs-up

0

Similar questions

Q. A lamp post is situated at the middle point

M

A C

of a triangular plot

A B C

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

A B = 9 m

. Lamp post subtends angle

15^{o}

B

. Determine the height of the lamp post.

Q. Consider a triangular plot

A B C

A B = 7 m

B C = 5 m

C A = 6 m

. A vertical lamp-post at the mid point

D

A C

subtends an angle

30^{o}

(i n m)

of the lamp-post is?

Q. Consider a triangular plot

A B C

A B = 7 m, B C = 5 m

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. Consider a triangle plot

A B C

A B = 7 m, B C = 5 m

C A = 6 m

. A vertical lamp--post at the mid point

D

A C

subtends an angle

30^{o}

B

(i n m)

of the lamp post is:

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Area

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Area of a Triangle

Standard VII Mathematics

Join BYJU'S Learning Program

CrossIcon