Question:
If the angles of a triangle are in the ratio 1 : 2 : 3, prove that its corresponding sides are in the ratio $1: \sqrt{3}: 2$
Solution:
Given: Angles of a triangle are in the ratio 1 : 2 : 3
Need to prove: Its corresponding sides are in the ratio $1: \sqrt{3}: 2$
Let the angles are $x, 2 x, 3 x$
Therefore, $x+2 x+3 x=180^{0}$
$6 x=180^{\circ}$
$x=30^{\circ}$
So, the angles are $30^{\circ}, 60^{\circ}, 90^{\circ}$
So, the ratio of the corresponding sides are:
$=\sin 30^{\circ}: \sin 60^{\circ}: \sin 90^{\circ}$
$=\frac{1}{2}: \frac{\sqrt{3}}{2}: 1$
$=1: \sqrt{3}: 2$ [Proved]
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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