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A helicopter, at $8000$ m altitude from the ground, passed vertically above second helicopter at an instance when the angles of elevation of the two helicopters from the same point on the ground are $60 °$ and $30 °$ respectively. What is the vertical distance between the two helicopters.

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Important Questions on Similarity, Right Triangles, and Trigonometry

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Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

\frac{\sec θ - \tan θ}{\sec θ + \tan θ}

= \frac{3}{5}

, then the value of

\frac{cosec θ + \cot θ}{cosec θ - \cot θ}

is:

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

5 \sin^{2} θ + 14 \cos θ = 13, 0^{o} < θ < 90^{o}

, then what is the value of

\frac{\sec θ + \cot θ}{cosec θ + \tan θ}

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

The value of the expression

cosec (85^{ο} + θ) - \sec (5^{ο} - θ) - \tan (55^{ο} + θ) + \cot (35^{ο} - θ)

is :

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

Seema flies a kite on a

16 m

string at an inclination of

60 °

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

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

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?

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

11 \sin^{2} θ - \cos^{2} θ + 4 \sin θ - 4 = 0, 0^{o} < θ < 90^{o}

, then what is the value of

\frac{\cos 2 θ + \cot 2 θ}{\sec 2 θ - \tan 2 θ}

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

\sec θ - \tan θ = \frac{x}{y}

(0 < x < y)

and

0^{ο} < θ < 90^{ο}

, then

\sin θ

is equal to :

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

If the height of a pole and the distance between the pole and a man standing nearby are equal, what would be the angle of elevation to the top of the pole?

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

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 - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

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?

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

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 _____.

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

In triangle

ABC

measure of angle

B

90 °

. If

\sec A = \frac{25}{7}

and

AB = 14 cm

, what is the length (in

cm

) of side

BC

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

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 _____.

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

2 \sin θ +15 \cos^{2} θ = 7, 0^{ο} < θ < 90^{ο}

, then

\tan θ + \cos θ + \sec θ =

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

The length of the shadow of a vertical pole on the ground is

36 m

. If the angle of elevation of the sun at that time is

θ

, such that

\sec θ = \frac{13}{12}

, then what is the height (in

m

) of the pole?

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

P

and

Q

are the 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^{°}

and

30^{°}

respectively and the distance between them is

84 \sqrt{3} m

. What is the height (in

m

) of the pole?

MEDIUM

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

A girl

1.2 m

tall can just see the sun over a

3.62 m

tall which is

2.42 m

away from her. The angle of elevation of the sun is:

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

The value of

\frac{\tan 30^{o} cosec 60^{o} + \tan 60^{o} \sec 30^{o}}{\sin^{2} 30^{o} + 4 \cot^{2} 45^{o} - \sec^{2} 60^{o}}

is:

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

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.

EASY

Mathematics>Geometry - III>Similarity, Right Triangles, and Trigonometry>Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles

∆ XYZ

, the measure of angle

Y

90 °

. If

\sec X = \frac{17}{8}

, and

XY = 0.8 cm

, what is the length (in

cm

) of side

XZ

A helicopter, at 8000 m altitude from the ground, passed vertically above second helicopter at an instance when the angles of elevation of the two helicopters from the same point on the ground are 60° and 30° respectively. What is the vertical distance between the two helicopters.

Important Questions on Similarity, Right Triangles, and Trigonometry

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A helicopter, at $8000$ m altitude from the ground, passed vertically above second helicopter at an instance when the angles of elevation of the two helicopters from the same point on the ground are $60 °$ and $30 °$ respectively. What is the vertical distance between the two helicopters.