B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 20 - Simple 2-D Problems in Right Triangle [Latest edition]

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

1. The height of the trapezium 
2. 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.

In ΔABC, ∠B = 90°, AB = 3 cm, AC = 6 cm, then θ = ______.

AC = 10 cm, ∠B = 90°, ∠C = 30°. ∴ AB = ______.

AB ⊥ BC, AC = 20 cm, CD = 5 cm, ∠ACB = 60°, AE = ______.

AD ⊥ BC, AB = 13 cm, BD = 12 cm, DC = 5 cm

sin x = ______.

AD ⊥ BC, AB = 13 cm, BD = 12 cm, DC = 5 cm

angle y = ______.

In the figure, angle θ = ______.

In the given figure, angle x = ______.

In the figure AB = 10 cm, ∠B = 30°, DC = 5 cm

AD = ______.

In the figure AB = 10 cm, ∠B = 30°, DC = 5 cm

angle θ = ______. 

In the figure PR is ______.

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`

Assertion (A): In the rectangle PQRS if PS = 4 cm and PR = 8 cm, then 9 = 30°.

Reason (R): tan 45° = 1

Assertion (A): In ABC, AB = 4 cm, BC = 6 cm then area of ΔABC= `6sqrt3  "cm"^2`.

Reason (R): Height = `2sqrt3` cm.

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"`

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

1. angles x
2. AC
3. 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:

1. AD
2. the perimeter of ΔABC.

In ΔABC, AD ⊥ BC, AB = 13 cm, BD = 5 cm, DC = 4 cm. Find the value of 

1. AD
2. 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.