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ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.

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#### Solution

Given that ΔRST ~ ΔUAY.

In ΔRST, RS = 6 cm, m∠S = 50°, ST = 7.5 cm.

Given that the corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4.

`therefore "RS"/"UA"="ST"/"AY"="RT"/"UY"=5/4;`

∠S =∠A = 50º

`therefore"RS"/"UA"=5/4`

`therefore6/"UA"=5/4`

`therefore(6xx4)/5="UA"`

`therefore "UA"=4.8 "cm"`

Similarly,

`"ST"/"AY"=5/4;`

`therefore7.5/"AY"=5/4`

`therefore(7.5xx4)/5="AY"`

`therefore"AY"=6" cm"`

Therefore, In ΔUAY, UA = 4.8 cm, AY = 6 cm and m∠A = 50°

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