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Mathematics, 17.05.2021 14:00 tristanortonubca

In triangle ABC, AB=c, BC=a, CA=b if b+c : c+a : a+b = 4 : 5 : 6, try to find
sin A : sin b : sin C.

ansver

Answers: 3

Show answers

Answers

ansver

Answer from: savingmayo

Step-by-step explanation:

Correct option is

B

AE

2

=

9

73

C

tanθ=

8

3

Hence

BD=DE=EC=

3

5

and △ABC is a right angled triangle.

Now

cosC=

2.AC.EC

AC

2

+EC

2

−AE

2

Or

AE

2

=AC

2

+EC

2

−2.AC.EC.cosC

Or

=4

2

+(

3

5

)

2

−2.8.

3

5

.cosC

=16+

9

25

−

3

2×4×5

.

5

4

Or

=

9

169

−

3

32

=

9

169−96

=

9

73

.

Hence

AE

2

=

9

73

.

cosθ=

2.AE.4

AE

2

+4

2

−

3

5

2

=

73

8

.

Hence

secθ=

8

73

Now

tanθ=

sec

2

θ−1

=

64

73

−1

=

8

3

.

solution

Expand-image

Correct option is

B

AE

2

=

9

73

C

tanθ=

8

3

Hence

BD=DE=EC=

3

5

and △ABC is a right angled triangle.

Now

cosC=

2.AC.EC

AC

2

+EC

2

−AE

2

Or

AE

2

=AC

2

+EC

2

−2.AC.EC.cosC

Or

=4

2

+(

3

5

)

2

−2.8.

3

5

.cosC

=16+

9

25

−

3

2×4×5

.

5

4

Or

=

9

169

−

3

32

=

9

169−96

=

9

73

.

Hence

AE

2

=

9

73

.

cosθ=

2.AE.4

AE

2

+4

2

−

3

5

2

=

73

8

.

Hence

secθ=

8

73

Now

tanθ=

sec

2

θ−1

=

64

73

−1

=

8

3

solution

Expand-image

ansver

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

ansver

Answer from: Quest

Igxtfuvu cube b kisooaokajsvd wkisvhikbg $26$

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