Breath Math

The Triangle and its Properties Exercise 6.3 – Class 7

The Triangle and its Properties Exercise 6.3 Questions:

Find the value of the unknown x in the following diagrams:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

2. Find the values of the unknown x and y in the following diagrams:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

The Triangle and its Properties Exercise 6.3 Solutions:

Find the value of the unknown x in the following diagrams:

(i)

(ii)

(iii)

(iv)

(v)

The Triangle and its Properties Exercise 6.2 – Class 7

The Triangle and its Properties Exercise 6.2 – Questions:

Find the value of the unknown exeterior angle x in the following diagrams:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Find the value of the unknown interior angle x in the following figure:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

The Triangle and its Properties Exercise 6.2 – Solutions:

Find the value of the unknown exterior angle x in the following…

The Triangle and its Properties Exercise 6.1 – Class VII

The Triangle and its Properties Exercise 6.1 – Questions:

In ∆ PQR, D is the mid pint of

PM is ______________________

PD is _______________________

Is QM = MR ?

  Draw rough sketch for the following:

In ∆ABC, BE is the median

In ∆PQR, PQ and PR are altitudes of the triangle.

In ∆XYZ, YL is an altitude in the exterior of the triangle.

Verify by drawing a diagram if the median and altitude of an…

Mensuration Exercise 15.6 – Questions

Draw a plan and calculate the area of a level ground using the information given below:

  Metre to C   To D 120

To E 180

220 210 120 80

200 to B

  From A  

  Plan out and find the area of the field from the date given from the Surveyor’s field book.

  Metre to C   To D 100 To C 75

To B 50

350 300 250 150 50 150 to F

100 to G

  From A  

  S…

Mensuration Exercise 15.5 – Class 10 – Solutions

Mensuration Exercise 15.5 – Questions

A petrol tank is in the shape of a cylinder with hemisphere of same radius attached to both ends. If the total length of the tank is 6m and the radius is 1m, what is the capacity of the tank in litres.

A rocket is in the shape of a cylinder with a cone attached to one end and a hemisphere attached to the other. All of them are of the same radius of 1.5m. The…

Mensuration Exercise15.4 – Class 10 – Solutions

Mensuration Exercise15.4 – Questions

Find the surface area of a sphere of radius 14 cm.

Find the TSA of a hemisphere of radius 5 cm.

A hemisphere bowl made of wood has inner diameter of 10.5 cm. Find the cost of painting it on the inside at the rate of Rs. 12 per 100 cm2.

Calculate the surface area of the largest sphere that can be cut out of a cube of side 15 cm.

Find the volume of the…

Mensuration Exercise 15.3 – Class 10

Mensuration Exercise 15.3 – Questions

1.Flower vase is in the form of a frustum of a cone. The perimeter of the ends are 44 cm and 8.4π cm. If the depth is 14 cm, fond how much water it can hold?

A bucket is in the shape of a frustum with the top and bottom circles of radii 15 cm and 10 cm. Its depth is 12 cm. Find its curved surface area and total surface area.(express your answer in terms of π)

Mensuration Exercise 15.2 – Class 10

Mensuration Exercise 15.2 – Questions

Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.

The radius of a cone is 7 cm and area of curved surface is 176 cm2. Find its slant height.

The area of the curved surface of a cone is 60πcm2. If the slant height of the cone is 8 cm, find the radius of the base.

Curved surface area of a cone is 308cm2…

Mensuration Exercise 15.1 – Class 10

Mensuration Exercise 15.1 – Questions:

The height of a right circular cylinder is 14 cm and the radius of its base is 2 cm. Find its (i) CSA (ii) TSA

An iron pipe 0 cm long has external radius equal to 12.5 cm and external radius equal to 11.5 cm. Find the TSA of the pipe.

The radii of two circular cylinders are in the ratio 2:# and the ratio of their curved surface areas is 5:6. Find the ratio…

Coordinate Geometry Exercise 14.4 – Class 10

Coordinate Geometry Exercise 14.4 – Questions:

In what ratio does the point (-2, 3) divide the line segment joining the points (-3, 5) and (4, -9)?

In the point C(1, 1) divides the line segment joining A(-2, 7) and B in the ratio 3:2, find the coordinates of B.

Find the ratio in which the point (-1, k) divides the line joining the points (-3, 10) and (6, -8) and find the value of k.

Find the…

Coordinate Geometry Exercise 14.3 – Class 10

Coordinate Geometry Exercise 14.3 – Questions:

Find the distance between the following pairs of points

(i) (8, 3) and (8,-7)

(ii) (1,-3) and (-4, 7)

(iii) (-4, 5) and (-12, 3)

(iv) 6, 5) and (4, 4)

(v) (2,0) and (0, 3)

(vi) (2, 8) and (6, 8)

 (vii) (a, b) and (c, b)

(viii) (cosθ, -sinθ) and (sinθ, -cosθ)

Find the distance between the origin and the point

(i) (-6, 8)

(ii) (5, 12)

(iii) (-8, 15)

Coordinate Geometry Exercise 14.2 – Class 10

Coordinate Geometry Exercise 14.2 – Questions:

Find the equation of the line whose angle of inclination and y-intercept are given.

(i) θ = 60˚, y-intercept is -2.

(ii) θ = 45˚, y-intercept is 3.

Find the equation of the line whose slope and y-intercept are given.

(i) Slope = 2, y-intercept = -4

(ii) Slope = –2/3, y-intercept = 1/2

(iii) Slope = -2, y-intercept = 3

Find the slope and y-intercept…

Coordinate Geometry Exercise 14.1 – Class 10

Coordinate Geometry Exercise 14.1 – Questions:

Find the slope of the curve whose inclination is

(i) 90˚

(ii) 45˚

(iii) 30˚

(iv) 0˚

Find the angles of inclination of straight lines whose slopes are

(i)√3

(ii) 1

(iii) 1/√3

Find the slope of the line joining the points

(i) (-4, 1) and (-5, 2)

(ii) 4, -8) and (5, -2)

(iii) (0, 0) and (√3, 3)

(iv) (-5, 0) and (0, -7)

(v) (2a, 3b) and (a, -b)

Find…

Trigonometry Exercise 13.5 – Class 10

Trigonometry Exercise 13.5 – Questions:

Find the value of ‘x’:

(i)

(ii)

(iii)

(iv)

(v)

II.

A tall building casts a shadow of 300 m long when the sun’s altitude (elevation) is 30˚. Find the height of the tower.

From the top o a building 50√3 m high, the angle of depression of an object on the ground is observed to be 45˚. Find the distance of the object from the building.

A tree is broken…

Trigonometry Exercise 13.4 – Class 10

Trigonometry Exercise 13.4 – Solutions:

Evaluate:

tan65˚/cot25˚

sin18˚/cos72˚

iii. cos48˚- sin42˚

cosec31˚ – sec59˚

cot34˚ – tan56˚

sin36˚/cos54˚ – sin54˚/cos36˚

vii. sec70˚ sin20˚ – cos70˚cosec20˚

viii. cos213˚ – sin277˚

  Prove that:

sin35˚ sin55˚ – cos35˚cos55˚ = 0

tan10˚tan15˚tan75˚tan80˚ = 1

iii. cos38˚cos52˚ – sin38˚sin52˚ = 0

  III. If sin5θ = cos4θ, where 4θ and 5θare acute…

Trigonometry Exercise 13.3 – Class 10

Trigonometry Exercise 13.3 – Questions:

Show that

(1 – sin2θ) sec2 θ = 1

(1 + tan2 θ) cos2 θ = 1

(1 + tan2 θ)(1 – sin θ)( 1 + sin θ) = 1

sin θ/(1+cosθ) + 1+cosθ/sinθ = 2 cosec θ

1 + sinθ/1 – sinθ = (sec θ + tan θ)2

cosA/1-tanA + sinA/1 – cotA = sinA + cosA

(1 – tan2A)/(1+tan2A) = 1 – 2sin2A

(sinθ + cosθ)2 = 1 + 2sinθcosθ

sinA cosA tanA + cosA.sinA.cotA = 1

(tanA – sinA)/(sin2A) = tanA/…

Trigonometry Exercise 13.2 – Class X

Trigonometry Exercise 13.2 – Questions:

I. Answer the following questions:

What trigonometric ratios of angles from 0 to 90 are equal to 0?

Which trigonometric ratios of angles from 0 to 90 are equal to 1?

Which trigonometric ratios of angles from 0 to 90 are equal to 1/2?

Which trigonometric ratios of angles from 0 to 90 are not defined?

Which trigonometric ratios of angles from 0 to 90 are…