(a) The sides PQ and PR of \(\Delta\) PQR are produced to T and S respectively, such that TQR = 131° and < QRS = 98°. Find < QPR.
(b) The circumference of a circular track is 400m. Find its radius, correct to the nearest metre. [Take \(\pi = \frac{22}{7}\)]
(b) The circumference of a circular track is 400m. Find its radius, correct to the nearest metre. [Take \(\pi = \frac{22}{7}\)]
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Correct Answer: Option n
Explanation:
(a)
< PQR = 180° - 131° = 49° (angles on a straight line)
\(\therefore < PQR = 49°\)
Also, \(< PQR = 180° - 98° = 82°\)
\(\therefore < QPR = 180° - (49° + 82°) = 180° - 131°\)
= \(49°\)
(b) Circumference of the circular track = \(2\pi r\)
\(\therefore 2\pi r = 400 \)
where \(\pi = \frac{22}{7}\)
\(\therefore r = \frac{400 \times 1 \times 7}{22 \times 2} = \frac{700}{11}\)
= \(63.63m \approxeq 64m\)
(a)
< PQR = 180° - 131° = 49° (angles on a straight line)
\(\therefore < PQR = 49°\)
Also, \(< PQR = 180° - 98° = 82°\)
\(\therefore < QPR = 180° - (49° + 82°) = 180° - 131°\)
= \(49°\)
(b) Circumference of the circular track = \(2\pi r\)
\(\therefore 2\pi r = 400 \)
where \(\pi = \frac{22}{7}\)
\(\therefore r = \frac{400 \times 1 \times 7}{22 \times 2} = \frac{700}{11}\)
= \(63.63m \approxeq 64m\)