In two right triangles ΔABC and ΔDEF,if sinB = sin E then prove that angle B = angleE - Future Study Point

In two right triangles ΔABC and ΔDEF,if sinB = sin E then prove that angle B = angleE

Trigonometry question,imp

In two right triangles ΔABC and ΔDEF,if sinB = sin E then prove that ∠ B = ∠E

 

Trigonometry question,imp

 

NCERT Solutions Class 10 Science from chapter 1 to 16

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Question.In two right triangles ΔABC and ΔDEF,if sinB = sin E then prove that angle B = angleE

ABC TRIANGLE

 

We are given two right triangles ΔABC and ΔDEF in which sinB =sinE

Let ∠A and ∠D are  right triangles of ΔABC and ΔDEF respectively

GIVEN : sinB = sinE

TO PROVE: ∠B =∠E

Proof: In ΔABC and ΔDEF

sinB = sinE

 

BC = kEF  & AC = kDF……(i)

Applying Pythagoras theorem in both triangles ΔABC and ΔDEF, we have

Putting the value of BC and AC in the equation  (i)

Since we have to prove the angles of two triangles, so we are needed to prove both triangles similar to each other.

And proving both triangles similar to each other, here we have to prove all three sides in proportional to each other.

From (i),(ii) and (iii) we have

∴ΔABC ∼ DEF (SSS rule)

Hence ∠B =∠E

OR

you can understand it through our video

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NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

 

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