Question

PQR is a triangle PQ is 19.5cm and QR is 11cm PS is the altitute of triangle PQR of lenght 5cm C is a circle circumscribing the triangle find thr radius

Answer 1

R = 18.14 cm if PQR is a triangle PQ is 19.5cm and QR is 11cm PS is the altitute of triangle PQR of lenght 5cm

Step-by-step explanation:

PQR is a triangle PQ is 19.5cm and QR is 11cm

PS altitude of triangle PQR of lenght 5cm

=> Sin∠Q  = PS/PQ  = 5/(19.5)

Cos∠Q  = √(1 - Sin²Q) =  √355.25‬ / 19.5

∠Q is subtended by chord PR

angle subtended by chord PR at center = 2∠Q

R = radius of circle

PR² = PQ²  + QR² - 2PQ.QRCos∠Q

PR² = R² + R²  - 2R²Cos2∠Q

=>  PQ²  + QR² - 2PQ.QRCos∠Q = 2R² ( 1  - Cos2∠Q)

=> 19.5² + 11²  -  2*19.5 * 11  * √355.25‬ / 19.5  = 4R² (25/380.25)

=> 380.25 + 121 -  22√355.25 = 100R²/380.25

=> R = 18.14 cm

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