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Two overlapping right triangles are shown below. What is the value of ‘ $x$ ’?

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Important Questions on Triangles

HARD

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

The angle of elevation of a cloud

C

from a point

P, 200 m

above a still lake is

30^{o}

. If the angle of depression of the image of

C

in the lake from the point

P

60^{o}

, then

P C

(in

m

) is equal to

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Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

X is $5 m$ tall and he notices that he casts a shadow that is $3 m$ long. He then measures that the shadow cast by his school building is $30 m$ long. How tall is the building?

HARD

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

A peacock perched on the top of a

12 m

high tree spots a snake moving towards its hole at the base of a tree from a distance equal to thrice the height of the tree. The peacock flies towards the snake in a straight line, and they both move at the same speed. At what distance from the base of the tree will peacock catch the snake?

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Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

Six consecutive sides of an equiangular octagon are

6, 9, 8, 7, 10, 5

in that order. The integer nearest to the sum of the remaining two sides is

EASY

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

The circle of radius

4 c m

and centre

O

has a tangent

P R

. If

∠ P O R = 90^{o}

and

O R = 7 c m

and

O P = 24 c m

. Calculate the length (in

c m

.) of

P R

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Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

A person standing on the top of a building of height

60 \sqrt{3}

feet observed the top of a tower to lie at an elevation of

45 ° .

That person descended to the bottom of the building and found that the top of the same tower is now at an angle of elevation of

60 ° .

The height of the tower (in feet) is

MEDIUM

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are

60^{o}

and

30^{o}

, respectively and the distance between them is

84 \sqrt{3} m

. What is the height (in

m

) of the pole?

EASY

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

Seema flies a kite on a

16 m

string at an inclination of

60 °

. What is the height of the kite above the ground?

HARD

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

A very tall tree breaks from the middle due to storm. The broken part of the tree did not separate from the tree and the top of the tree touched the ground at a distance of

12

metre from the base of the tree. If the tree broke at the height of

37

metre from the ground, then what is the length of the broken portion of the tree in metres?

EASY

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

Two poles of the height $12 m$ and $17 m$ stand vertically upright on a plain ground. If the distance between their feet is $12 m$ , find the distance between their tops.

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Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

From an external point

P

, a tangent

PQ

is drawn to a circle, with the centre

O

,touching the circle at

Q

. If the distance of

P

from the centre is

13 cm

and length of tangent

PQ

12 cm

, then the radius of the circle is

HARD

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point

A

on the path, he observes that the angle of elevation of the top of the pillar is

30^{°}

. After walking for

10

minutes from

A

in the same direction, at a point

B

, he observes that the angle of elevation of the top of the pillar is

60^{°}

. Then the time taken (in minutes) by him, from

B

to reach the pillar, is

HARD

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

∆ A B C, ∠ B = 90 °

. If points

D

and

E

are on the side

B C

such that

B D = D E = E C

, then which of the following is true?

HARD

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

Let

P Q R

be a triangle in which

P Q = 3

. From the vertex

R,

draw the altitude

R S

to meet

P Q

S

. Assume that

R S = \sqrt{3}

and

P S = Q R

. Then,

P R

equals

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Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

△ ABC, ∠ C = 90 °, AC = 5 cm

and

BC = 12 cm

. The bisector of

∠ A

meets

BC

D

. What is the length of

AD

?

MEDIUM

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

A ladder is resting against a wall. The angle between the foot of the ladder and the wall is

45 °

and the foot of the ladder is

6.6 m

away from the wall. The length of the ladder (in

m

) is _____.

MEDIUM

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

Let A and B be two towers with the same base. From the mid-point of the line joining their feet, the angles of elevation of the tops of A and B are

30 °

and

45 °

, respectively. The ratio of the heights of A and B is _____.

EASY

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

A ladder $10 m$ long is leaning against a vertical wall. It makes an angle of $60 °$ with the ground. How far is the foot of the ladder from the wall?

MEDIUM

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

Two vertical poles of height,

20 m

and

80 m

stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is:

HARD

Mathematics>Geometry>Triangles>Pythagoras Theorem and Its Proof

A sphere with centre $O$ sits atop a pole as shown in the figure. An observer on the ground is at a distance $50 m$ from the foot of the pole. She notes that the angles of elevation from the observer to points $P$ and $Q$ on the sphere are $30 °$ and $60 °$ , respectively. Then, the radius of the sphere in meters is

Question Image

Two overlapping right triangles are shown below. What is the value of ‘x’?

Important Questions on Triangles

Learn and Prepare for any exam you want !

Two overlapping right triangles are shown below. What is the value of ‘ $x$ ’?