Theory question 103
Triangles and Quadrilaterals(a) In the diagram below, 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. Their 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 π = 22/7].
Show the model answer
Model answer
(a) Opposite sides of a parallelogram are equal: |PQ| = |RS| = 3 cm and |YZ| = |RS| = 3 cm
|PZ| = 3 + 2 + 3 = 8 cm
(b) Difference in longitude = 95° − 25° = 70°
PQ = 70/360 × 2 × 22/7 × 6400 × cos 56°
= 7822.2 × 0.5592 ≈ 4374 km
Explanation
Along a parallel of latitude, use radius R cos(latitude).