Question

Angles Q and R of A PQR are 47° and 43°. Write which of t true: (a) PQ2 + QR2 = RP2 (b) PQ2 + PR2 = OR? (c) RP2 + QR2 = PQ2​​

Answer 1

Answer:

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Step-by-step explanation:

Angles Q and R of a ∆PQR are 25º and 65º. Write which of the following is true:

(i)PQ2 + QR2 = RP2

(ii)PQ2 + RP2 = QR2

(iii)RP2 + QR2 = PQ2



Solution:

From the figure we see that the two angles of a triangle are given and we must find out the third angle by using the angle sum property that is the sum of three interior angles of a triangle is 180°.

We know that, sum of interior angles of a triangle is 180°.

∠P + ∠Q + ∠R = 180°

∠P + 25° + 65° = 180°

∠P + 90° = 180°

∠P = 180° - 90°

∠P = 90°

Thus, triangle PQR is a right angled at P

As one of the angles is 90° that means it is a right-angled triangle and the square of the hypotenuse is equal to the sum of the square of the other two sides.

Therefore, by Pythagoras theorem,

(Perpendicular)2 + (Base)2 = (Hypotenuse )2

Here, Perpendicular = QP, Base = PR and Hypotenuse = QR

(QP)2 + (PR)2 = (QR)2

Hence, option (ii) is correct.

Answer 2

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(b) (PQ)² + (PR)² = (QR)²

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Sum of all angles of a triangle is 180°. Here, the third angle P is:-

$180 - (47 + 43) = 180 - 90 = 90°$

So, the third angle is 90°. So, it is a right angled triangle which is right angled at P (Because, P is the unknown angle here). Then, always lines from point P will be squared to obtain the sum of square of other two sides:-

(PQ)² + (PR)² = (QR)² (b)

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