Q. 55.0( 1 Vote )
Q and R of a triangle PQR are 25° and 65°. Is PQR a right-angled triangle? Moreover, PQ is 4cm and PR is 3 cm. Find QR.
In ΔPQR, ∠Q = 25° and ∠R = 65°.
We know that sum of angles of a triangle = 180°.
⇒ ∠P + ∠Q + ∠R = 180°
⇒ ∠P + 25° + 65° = 180°
⇒ ∠P = 180° - 90°
∴ ∠P = 90°
∴ Δ PQR is a right angled triangle which is right angled at P.
Given, PQ = 4 cm and PR = 3 cm
We know that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
⇒ In ΔPQR, QR2 = PQ2 + PR2
⇒ QR2 = 42 + 32
= 16 + 9
∴ QR = √25 = 5 cm
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