ABSTRACT
Problem 1. In Fig. 21.2, find the length of EF.
By Pythagoras’ theorem: e2 D d2 C f2 Hence 132 D d2 C 52
169 D d2 C 25 d2 D 169 25 D 144
Thus d D p
144 D 12 cm i.e. EF= 12 cm
Problem 2. Two aircraft leave an airfield at the same time. One travels due north at an average speed of 300 km/h and the other due west at an average speed of 220 km/h. Calculate their distance apart after 4 hours
After 4 hours, the first aircraft has travelled 4 ð 300 D 1200 km, due north, and the second aircraft has travelled 4ð220 D 880 km due west, as shown in Fig. 21.3. Distance apart after 4 hours D BC. From Pythagoras’ theorem:
BC2 D 12002 C 8802 D 1 440 000 C 7 74 400 and
BC D p
2 214 400
Now try the following exercise
Exercise 78 Further problems on the theorem of Pythagoras
1. In a triangle CDE, D D 90°, CD D 14.83 mm and CE D 28.31 mm. Determine the length of DE. [24.11 mm]
2. Triangle PQR is isosceles, Q being a right angle. If the hypotenuse is 38.47 cm find (a) the lengths of sides PQ and QR, and (b) the value of 6 QPR.
