Mathematics Theory ABC is a triangle, right-angled at C. P is the mid-point of AC,

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.

Explanation

Let |PC| = x cm; Hence, |AC| = 2x cm

(tan 37° = frac{x}{5})

(x = 5 tan 37 )

(x = 3.768 cm)

(therefore |AC| = 2 times 3.768)

= (7.536 cm)

(approxeq 7.54 cm) (3 sig. figs)

(b) From (Delta ABC), 

(tan < ABC = frac{7.536}{5} = 1.5072)

(< ABC = tan^{-1} (1.5072) = 56.436°)

(therefore < PBA = < ABC – < PBC)

= (56.436° – 37°)

= (19.436° approxeq 19.44°)