ABC is a triangle, right-angled at C. P is the mid-point of AC, < PBC = 37° and |BC| = 5 cm. Calculate : (a) |AC|, correct to 3 significant figures ; (b) < ...
Assessment:WAEC SSCE - General Mathematics - 1999Subject:General Mathematics
ABC is a triangle, right-angled at C. P is the mid-point of AC, < PBC = 37° and |BC| = 5 cm. Calculate :
(a) |AC|, correct to 3 significant figures ;
(b) < PBA.
In \(\triangle PBC\), the right angle is at \(C\), \(|BC|=5\text{ cm}\), \(\angle PBC=37^{\circ}\), and \(P\) is the midpoint of \(AC\).
(a) \[\tan37^{\circ}=\frac{PC}{BC}\Rightarrow PC=5\tan37^{\circ}=5\times0.7536=3.768\text{ cm}.\] Since \(P\) is the midpoint, \(|AC|=2\times PC=7.536\approx\) 7.54 cm (3 s.f.).
In \(\triangle PBC\), the right angle is at \(C\), \(|BC|=5\text{ cm}\), \(\angle PBC=37^{\circ}\), and \(P\) is the midpoint of \(AC\).
(a) \[\tan37^{\circ}=\frac{PC}{BC}\Rightarrow PC=5\tan37^{\circ}=5\times0.7536=3.768\text{ cm}.\] Since \(P\) is the midpoint, \(|AC|=2\times PC=7.536\approx\) 7.54 cm (3 s.f.).