Theory question 103
TrigonometryABC is a triangle right-angled at C. P is the mid-point of AC, ∠PBC = 37° and |BC| = 5cm. Calculate: (a) |AC| correct to 3 significant figures (b) ∠PBA.
Show the model answer
Model answer
(a) In triangle PBC: PC = 5 tan 37° = 5 × 0.7536 = 3.768 cm.
AC = 2 × PC = 7.536 ≈ 7.54 cm.
(b) tan ∠ABC = AC/BC = 7.536/5 = 1.507, so ∠ABC ≈ 56.4°.
∠PBA = ∠ABC − ∠PBC = 56.4 − 37 = 19.4°.
Explanation
∠PBA is the part of angle B between BA and BP, so subtract 37° from the whole angle at B.