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Question
PR = 26 cm, QR = 24 cm, ∠PAQ = 90°, PA = 6 cm and QA = 8 cm. Find ∠PQR
Options
80°
85°
75°
90°
Solution
90°
Explanation;
Hint:
PR = 26 cm, QR = 24 cm, ∠PAQ = 90°
In the ∆PQR,
PQ = `sqrt("PR"^2 - "QR"^2)`
= `sqrt(26^2 - 24^2)`
= `sqrt(676 - 576)`
= `sqrt(100)`
= 10
In the right ∆APQ
PQ2 = PA2 + AQ2
= 62 + 82
= 36 + 64
= 100
PQ = `sqrt(100)`
= 10
∆PQR is a right angled triangle at Q.
Since PR2 = PQ2 + QR2
∠PQR = 90°
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