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4 years ago

Dan, Gordon and Malachy share some sweets in the ratio 4:3:5. Dan gets 48 sweets. How many sweets are there altogether?

Mathematics

1 answer:

Mrac [35]4 years ago

3 0

Answer:

144 sweets

Step-by-step explanation:

Let

x----> number of sweets that Dan has

y----> number of sweets that Gordon has

z----> number of sweets that Malachy has

we know that

x=48

x/y=4/3----> y/x=3/4 ----> y=(3/4)x

Substitute the value of x

y=(3/4)48=36

x/z=4/5 ----> z/x=5/4 ----> z=(5/4)x

Substitute the value of x

z=(5/4)48=60

therefore

altogether there are x+y+z=48+36+60=144 sweets

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denis-greek [22]

Answer:

______________________________________________________

TRIGONOMETRY IDENTITIES TO BE USED IN THE QUESTION :-

For any right angled triangle with one angle α ,

$\cos (90 - \alpha ) = \sin \alpha$ or $\sin(90 - \alpha ) = \cos\alpha$

$cosec \: (90 - \alpha ) = \sec\alpha$ or $\sec(90 - \alpha ) = cosec\:\alpha$

SOME GENERAL TRIGNOMETRIC FORMULAS :-

$\sin \alpha = \frac{1}{cosec \: \alpha }$ or $cosec \: \alpha = \frac{1}{\sin \alpha }$

$\cos \alpha = \frac{1}{\sec \alpha }$ or $\sec \alpha = \frac{1}{\cos \alpha }$

______________________________________________________

Now , lets come to the question.

In a right angled triangle , let one angle be α (in place of theta) .

So , lets solve L.H.S.

$\cos (90 - \alpha ) \times cosec(90 - \alpha )$

$=> sin\alpha \times \sec\alpha$

$=> \sin\alpha \times \frac{1}{\cos\alpha }$

$=> \frac{\sin\alpha }{\cos\alpha }$

$=> \tan\alpha$ = R.H.S.

∴ L.H.S. = R.H.S. (Proved)

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