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Chapters
1: Rational and Irrational Numbers
UNIT-II: COMMERCIAL MATHEMATICS
2: Compound Interest
UNIT-III: ALGEBRA
3: Expansions
4: Factorisation
5: Simultaneous Linear Equations
6: Indices
7: Logarithms
UNIT-IV: GEOMETRY
8: Triangles
9: Inequalities
10: Mid-point Theorem
11: Pythagoras Theorem
12: Rectilinear Figures (Theorems on Parallelograms and Construction of Polygons)
13: Theorems on Area
14: Circles (Chord and Arc Properties)
UNIT-V: STATISTICS
15: Statistics
16: Graphical Representation of Statistical Data
UNIT-VI: MENSURATION
17: Mensuration
18: Surface Area and Volume of Solids
UNIT-VII: TRIGONOMETRY
19: Trigonometry
▶ 20: Simple 2-D Problems in Right Triangle
UNIT-VIII: COORDINATE GEOMETRY
21: Coordinate Geometry
![B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 20 - Simple 2-D Problems in Right Triangle - Shaalaa.com](/images/mathematics-english-class-9-icse_6:a927b361d63845f4b2afea4ec6bbe35a.jpg "B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 20 - Simple 2-D Problems in Right Triangle")
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Solutions for Chapter 20: Simple 2-D Problems in Right Triangle
Below listed, you can find solutions for Chapter 20 of CISCE B Nirmala Shastry for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 20 Simple 2-D Problems in Right Triangle EXERCISE 20 [Pages 243 - 244]
Find the length of x and y in the following figure.
Find the length of x and y in the following figure.
Find the length of x and y in the following figure.
Find the area of rhombus ABCD in which AB = 6 cm and ∠ABC = 60°.
In a rhombus ABCD, ∠A = 60°, AB = 10 cm. Find the length of the diagonals.
In the given parallelogram ABCD, AB = 10 cm, BC = 15 cm and ∠ABC = 30°. Find the area of ABCD.
In the trapezium ABCD, AB || DC and ∠C = 60°, ∠D = 45°. If AB = 6 cm and BC = 4 cm, find
- The height of the trapezium
- Length of DC
In ABC, AB = 6 cm, BC = 8 cm and ∠ABC = 150°. Find the area of ΔABC.
[Hint: Drop AP ⊥ CB extended.]
In ΔPQR, PS is perpendicular to QR. If PS = 6 cm, find the length of QR.
In ΔABC, ∠B = 90° and ∠A is double ∠C. Find `(AB)/(AC)`.
In ΔPQR, ∠P : ∠Q : ∠R = 1 : 2 : 3 and altitude from P to QR is 4 cm. Find the perimeter of ΔPQR.
In a rectangle ABCD, T is a point on AD such that ∆BTC is equilateral. If BC = 4 cm, find the area of ABCD.
A ladder makes an angle of 60° with the floor and its lower end is 2 m from the wall. What is the length of the ladder? At what height is it touching the wall?
A boy is flying a kite at a height of 40 m from the ground, attached to a string inclined at 30° to the horizontal. Find the length of the string.
ABC is an equilateral triangle inscribed in a circle with centre 0. Radius OB = 4 cm, and OM is perpendicular to BC. Find x and the perimeter of the triangle.
In the rectangle ABCD, the diagonals intersect at O. If ∠COD = 120° and AB = 6 cm, OP is perpendicular to AB. Find x, y, BC and AC.
In ΔABC, BD ⊥ AC. ∠A = 45°, ∠C = 30° and BC = 20 cm. Find the length of (i) BD and (ii) AB.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 20 Simple 2-D Problems in Right Triangle MULTIPLE CHOICE QUESTIONS [Pages 244 - 245]
In ΔABC, ∠B = 90°, AB = 3 cm, AC = 6 cm, then θ = ______.
30°
45°
60°
none of these
AC = 10 cm, ∠B = 90°, ∠C = 30°. ∴ AB = ______.
`5sqrt3` cm
`5sqrt2`
5 cm
`5/sqrt3 "cm"`
AB ⊥ BC, AC = 20 cm, CD = 5 cm, ∠ACB = 60°, AE = ______.
`10sqrt3` cm
`(10sqrt3 + 5)` cm
`(10sqrt3 − 5)` cm
15 cm
AD ⊥ BC, AB = 13 cm, BD = 12 cm, DC = 5 cm
sin x = ______.
`5/13`
`12/13`
`12/5`
`5/12`
AD ⊥ BC, AB = 13 cm, BD = 12 cm, DC = 5 cm
angle y = ______.
60°
30°
45°
none of these
In the figure, angle θ = ______.
30°
45°
60°
none of these
In the given figure, angle x = ______.
30°
45°
60°
none of these
In the figure AB = 10 cm, ∠B = 30°, DC = 5 cm
AD = ______.
10 cm
20 cm
5 cm
7.5 cm
In the figure AB = 10 cm, ∠B = 30°, DC = 5 cm
angle θ = ______.
30°
45°
60°
none of these
In the figure PR is ______.
18 cm
`3sqrt3` cm
`6sqrt3` cm
`9sqrt3` cm
Direction for Questions 9 to 12: In each of the following questions, a statement of assertion (A) is given and a statement of Reason (R) given below it choose the correct option for each question.
Assertion (A): ΔABC is equilateral with side 3 cm If AD = 1 cm then EC = 1 cm, ∠ADE = 90°
Reason (R): cos 60° = `(AD)/(AE) = 1/2`
Both A and R are true, and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion (A): In the rectangle PQRS if PS = 4 cm and PR = 8 cm, then 9 = 30°.
Reason (R): tan 45° = 1
Both A and R are true, and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion (A): In ABC, AB = 4 cm, BC = 6 cm then area of ΔABC= `6sqrt3 "cm"^2`.
Reason (R): Height = `2sqrt3` cm.
Both A and R are true, and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
Assertion (A): If a ladder makes an angle of 30° with the wall and its lower end is 1.5 m from the wall, then the length of the ladder is 3 m.
Reason (R): cos 60° = `1.5/"length of ladder"`
Both A and R are true, and R is the correct reason for A.
Both A and R are true but R is the incorrect reason for A.
A is true but R is false.
A is false but R is true.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 20 Simple 2-D Problems in Right Triangle MISCELLANEOUS EXERCISE [Pages 246 - 247]
In the rectangle PQRS, ∠SQR = 60° and QR = 4 cm. Find SR and QS.
In ΔABC, AD ⊥ BC, AB = 60 cm, AD = 30 cm, and ∠C = 45°. Find
- angles x
- AC
- BC
The length of a string attached to a kite and a point on the ground is 58 m. If the string makes an angle A with the ground such that tan A = `20/21` at what height is the kite?
At the base of ΔABC is the rectangle BCDE, CD = 3 cm, AC = 12 cm, and ∠ACB = 30°. Find the length of AE.
In rectangle ABCD, DB = 10 cm and BC = 5 cm. Find ∠BDC and the length of AB.
In ABC, P is a point on AB such that ∠PCB = 45°, ∠B = 90°, and ∠ACB = 60°. Find the length of AP if BC = 10 cm.
In ΔABC, AD ⊥ BC. BC = 100 cm, tan B = `2/3` and tan C = `6/11`. Find the length of AD.
Find x and y in the given figure.
In ΔABC, ∠B = 90°, ∠C = 30° and AC = 16 cm. Find the lengths of AB and BC.
In ΔPQR, PQ2 + QR2 = PR2 and PR = 2QR. Write the measures of the angles of the triangle.
ABCD is a rectangle. P is the midpoint of BC, AP = 8 cm. Find the sides AB and BC.
ABC is an equilateral triangle, BD ⊥ AC, BD = `5sqrt3`. Find:
- AD
- the perimeter of ΔABC.
In ΔABC, AD ⊥ BC, AB = 13 cm, BD = 5 cm, DC = 4 cm. Find the value of
- AD
- tan x + cot y
In ΔPQR, PT ⊥ QR, PQ = 10 cm, QT = 6 cm, TR = 15 cm. Find the value of sin x + tan y.
Solutions for 20: Simple 2-D Problems in Right Triangle
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 20 - Simple 2-D Problems in Right Triangle
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