a pole stands vertically inside a triangular park abc if

A pole stands vertically inside a triangular park $$ABC.$$ If the angle of elevation of the top of the pole from each corner of the park is same, then the foot of the pole is at the

A. centroid

B. circumcentre

C. incentre

D. orthocentre

Answer : centroid

Solution :
The foot of the pole is at the centroid. Because centroid is the point of intersection of medians $$AD, BE$$ and $$CF,$$ which are the lines joining a vertex with the mid point of opposite side.
Properties and Solutons of Triangle mcq solution image

Properties and Solutons of Triangle mcq solution image

Releted MCQ Question on
Trigonometry >> Properties and Solutons of Triangle

Releted Question 1

If the bisector of the angle $$P$$ of a triangle $$PQR$$ meets $$QR$$ in $$S,$$ then

A. $$QS = SR$$

B. $$QS : SR = PR : PQ$$

C. $$QS : SR = PQ : PR$$

D. None of these

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Releted Question 2

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is 15°. The distance of the boat from the foot of the light house is

A. $$\left( {\frac{{\sqrt 3 - 1}}{{\sqrt 3 + 1}}} \right)60\,{\text{metres}}$$

B. $$\left( {\frac{{\sqrt 3 + 1}}{{\sqrt 3 - 1}}} \right)60\,{\text{metres}}$$

C. $${\left( {\frac{{\sqrt 3 + 1}}{{\sqrt 3 - 1}}} \right)^2}{\text{metres}}$$

D. none of these

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Releted Question 3

In a triangle $$ABC,$$ angle $$A$$ is greater than angle $$B.$$ If the measures of angles $$A$$ and $$B$$ satisfy the equation $$3\sin x - 4{\sin ^3}x - k = 0, 0 < k < 1,$$ then the measure of angle $$C$$ is

A. $$\frac{\pi }{3}$$

B. $$\frac{\pi }{2}$$

C. $$\frac{2\pi }{3}$$

D. $$\frac{5\pi }{6}$$

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Releted Question 4

In a triangle $$ABC,$$ $$\angle B = \frac{\pi }{3}{\text{ and }}\angle C = \frac{\pi }{4}.$$ Let $$D$$ divide $$BC$$ internally in the ratio 1 : 3 then $$\frac{{\sin \angle BAD}}{{\sin \angle CAD}}$$ is equal to

A. $$\frac{1}{{\sqrt 6 }}$$

B. $${\frac{1}{3}}$$

C. $$\frac{1}{{\sqrt 3 }}$$

D. $$\sqrt {\frac{2}{3}} $$

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A pole stands vertically inside a triangular park $$ABC.$$ If the angle of elevation of the top of the pole from each corner of the park is same, then the foot of the pole is at the

Releted MCQ Question on
Trigonometry >> Properties and Solutons of Triangle

If the bisector of the angle $$P$$ of a triangle $$PQR$$ meets $$QR$$ in $$S,$$ then

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is 15°. The distance of the boat from the foot of the light house is

In a triangle $$ABC,$$ angle $$A$$ is greater than angle $$B.$$ If the measures of angles $$A$$ and $$B$$ satisfy the equation $$3\sin x - 4{\sin ^3}x - k = 0, 0 < k < 1,$$ then the measure of angle $$C$$ is

In a triangle $$ABC,$$ $$\angle B = \frac{\pi }{3}{\text{ and }}\angle C = \frac{\pi }{4}.$$ Let $$D$$ divide $$BC$$ internally in the ratio 1 : 3 then $$\frac{{\sin \angle BAD}}{{\sin \angle CAD}}$$ is equal to

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Properties and Solutons of Triangle

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A pole stands vertically inside a triangular park $$ABC.$$ If the angle of elevation of the top of the pole from each corner of the park is same, then the foot of the pole is at the

Releted MCQ Question on Trigonometry >> Properties and Solutons of Triangle

If the bisector of the angle $$P$$ of a triangle $$PQR$$ meets $$QR$$ in $$S,$$ then

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is 15°. The distance of the boat from the foot of the light house is

In a triangle $$ABC,$$ angle $$A$$ is greater than angle $$B.$$ If the measures of angles $$A$$ and $$B$$ satisfy the equation $$3\sin x - 4{\sin ^3}x - k = 0, 0 < k < 1,$$ then the measure of angle $$C$$ is

In a triangle $$ABC,$$ $$\angle B = \frac{\pi }{3}{\text{ and }}\angle C = \frac{\pi }{4}.$$ Let $$D$$ divide $$BC$$ internally in the ratio 1 : 3 then $$\frac{{\sin \angle BAD}}{{\sin \angle CAD}}$$ is equal to

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Trigonometry >> Properties and Solutons of Triangle

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Properties and Solutons of Triangle