(a) In the diagram, PQSR and SRYZ are parallelograms and PQYZ is a straight line. If /QY/ = 2cm and /RS/ = 3cm, find /PZ/.
(b) P and Q are two towns on the earth’s surface on latitude 56°N. Thei longitudes are 25°E and 95°E respectively. Find the distance PQ along their parallel of latitude, correct to the nearest km. [Take radius of the earth as 6400km and (pi = frac{22}{7})]
Explanation
(a) (/QY/ = 2cm; /RS/ = 3cm)
(therefore /YZ/ = /RS/ = /PQ/ = 3cm) (opp sides of a parallelogram)
But (/PZ/ = /PQ/ + /QY/ + /YZ/)
(therefore /PZ/ = 3cm + 2cm + 3cm = 8cm)
(b) Difference in longitude = 95° – 25° = 70°
Distance PQ = (frac{70}{360} times 2pi R cos theta)
= (frac{70}{360} times 2 times frac{22}{7} times 6400 cos 56)
= (frac{7}{36} times 2 times frac{22}{7} times 6400 times 0.5592)
= (4374.19 km approxeq 4374 km) (to the nearest km)