SSC (English Medium) 9th Standard - Maharashtra State Board Question Bank Solutions for Geometry

In the right angled Δ XYZ, ∠XYZ = 90^° and a, b, c are the lengths of the sides as shown in the figure. Write the following ratios,

1. sin X
2. tan Z
3. cos X
4. tan X.

In right angled ΔLMN, ∠LMN = 90°, ∠L = 50° and ∠N = 40°, write the following ratios.

1. sin 50°
2. cos 50°
3. tan 40°
4. cos 40°

In the given figure, ∠PQR = 90°, ∠PQS = 90°, ∠PRQ = α and ∠QPS = θ Write the following trigonometric ratios.

1. sin α, cos α, tan α
2. sin θ, cos θ, tan θ

In the given figure, `angle` PQR = 90^° , `angle` PQS = 90^° , `angle` PRQ = θ and `angle`  QPS = θ   Write the following trigonometric ratios.

(i) sin θ, cos θ, tan θ
(ii) sin θ , cos θ , tan θ 

In the given figure, ∠ACD is an exterior angle of ΔABC. ∠B = 40°, ∠A = 70°. Find the measure of ∠ACD.

In ΔPQR, ∠P = 70°, ∠Q = 65° then find ∠R. 

The measures of angles of a triangle are x°, (x − 20)°, (x − 40)°. Find the measure of each angle.

The measure of one of the angles of a triangle is twice the measure of its smallest angle and the measure of the other is thrice the measure of the smallest angle. Find the measures of the three angles.

In the given figure, measures of some angles are given. Using the measures find the values of x, y, z. 

In the given figure, line AB || line DE. Find the measures of ∠DRE and ∠ARE using given measures of some angles. 

In Δ ABC, bisectors of ∠A and ∠B intersect at point O. If ∠C = 70°. Find the measure of ∠AOB. 

In the given Figure, line AB || line CD and line PQ is the transversal. Ray PT and ray QT are bisectors of ∠BPQ and ∠PQD respectively. Prove that m∠PTQ = 90°.

Using the information shown in figure, find the measures of ∠a, ∠b and ∠c.

In the given figure, line DE || line GF, ray EG and ray FG are bisectors of ∠DEF and ∠DFM respectively. Prove that, 

1. ∠DEG = `1/2∠"EDF"`
2. EF = FG

In right angled ΔTSU, TS = 5, ∠S = 90°, SU = 12 then find sin T, cos T, tan T. Similarly find sin U, cos U, tan U.

In right angled ΔYXZ, ∠X = 90°, XZ = 8 cm, YZ = 17 cm, find sin Y, cos Y, tan Y, sin Z, cos Z, tan Z.

In right angled ΔLMN, if ∠N =θ, ∠M = 90, cos θ =`24/25`, find sin θ and tan θ Similarly, find (sin² θ) and (cos² θ).

Volume of a cuboid is 34.50 cubic metre. Breadth and height of the cuboid is 1.5m and 1.15m respectively. Find its length.

To make an open fish tank, a glass sheet of 2 mm gauge is used. The outer length, breadth and height of the tank are 60.4 cm, 40.4 cm and 40.2 cm respectively. How much maximum volume of water will be contained in it?

Construct ΔPQR, in which QR = 4.2 cm m∠Q = 40° and PQ + PR = 8.5 cm