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REFER TO PHOTO, WILL GIVE 90 POINTS

REFER TO PHOTO, WILL GIVE 90 POINTS-example-1
User PGreen
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Answer:

  • RS = 7cm .

Explanation:

To find:-

  • The value of RS .

Answer:-

Let us take that, PQ = s , QS = p , QR = a and RS = b.

Here we can see that, ∆PQR and ∆PQS are right angled triangles .

Here, the value of RS would be,


\longrightarrow b = p - a \\

Finding the value of "p" :-

In ∆PQS ,


\longrightarrow \tan 45^o =(perpendicular)/(base) \\


\longrightarrow 1 = (72cm)/(p)\\


\longrightarrow \large \pmb { p = 72cm }\\

Finding the value of "a" :-

In ∆PQR , we can use Pythagoras theorem .

  • According to which, in a right angled triangle, the sum of squares of base and perpendicular is equal to the square of hypotenuse.
  • Hypotenuse is the longest side of the triangle and the side opposite to 90° is hypotenuse.

So that,


\longrightarrow\Large \pmb{\boxed{ p^2 + b^2 = h^2 }}\\

where the symbols have their usual meaning.

On substituting the respective values, we have;


\longrightarrow 72^2 + a^2 = 97^2 \\


\longrightarrow a^2 = 97^2-72^2 \\


\longrightarrow a^2 = 9409 - 5184 \\


\longrightarrow a^2 = 4225 \\


\longrightarrow a =√(4225)\\


\longrightarrow \large\pmb{ a = 65\ cm } \\

Hence we can find the value of b as ,


\longrightarrow b = p-a \\


\longrightarrow b = 72cm - 65cm\\


\longrightarrow b = 7cm \\


\longrightarrow\large\pmb{\underline{\boxed{\pmb{ \overline{RS} = 7cm }}}}\\

Therefore the value of RS is 7cm .

User Rafek
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