2) In the figure, angle Q = 90°,
angle P = angle R = 45°, then PR
=
Answers
Answer:
p=45°
Step-by-step explanation:
if q=90
then PQR IS A RIGHT ANGLED TRIANGLE
THERE FORE BY APPLYING CONCEPT OF ANGLE SUM PROPERTY
THEREFORE
^Q+^R+^P=180°
90+45+^P=180°
135+^P=180°
^P=180-135=45°
^P=45°
THEN PR IS THE HYPOTENUSE
P+R=90°
Given : angle Q = 90°, angle P = angle R = 45°
PQ = 5
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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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