a. In the diagram above, 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 of 56^\circN. Their longitudes are 25^\circE and 95^\circE, respectively. Find the distance PQ along their parallel of latitude, correct to the nearest km. [Take radius of the earth as 6400 km and \pi = \(\frac{22}{7}\)]
Attached Figure / Diagram
Verified Correct Answer: .
Step-by-Step Mathematical Solution
a. From the figure: |PZ| = |PQ| + |QY| + |YZ|
|PQ| = |RS| = 3 cm (opposite sides of a parallelogram)
|YZ| = |RS| = 3 cm (opposite sides of a parallelogram)
|QY| = 2 cm (given)
|PZ| = |PQ| + |QY| + |YZ|
|PZ| = 3 + 2 + 3 = 8 cm
b. radius of latitude r = R cos \alpha,
where \alpha is the angle 56º
r = 6400 cos 56^\circ = 3578.8 km
< PLQ = 95º - 25^\circ = 70^\circ
Length of arc PQ = \(\frac{\theta}{360}\) \times 2\pir
= \(\frac{70}{360}\) \times 2 \times (\(\frac{22}{7}\)) \times 3578.8 = \(\frac{39367.2}{9}\) = 4374 km
Source: Myschool Past Questions Archive (Record #75921)