in triangle PQR , angle Q=90°, PQ=5 , ANGLE P = ANGLE R = 45° then PR =?
Answers
Answer:
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Given : angle Q = 90°, angle P = angle R = 45°
PQ = 5
To Find : PR
Solution:
Angle P = angle R = 45°
Sides opposites to equal angles in a traingle are equal
Hence QR = PQ = 5
Using Pythagorean theorem:
square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.
PR² = PQ² + QR²
=> PR² = 5² + 5²
=> PR = 5√2
Another method
Cos ∠P = PQ / PR
=> Cos 45° = 5/PR
=> 1/√2 = 5/PR
=> PR = 5√2
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