Mensuration & Trigonometry

In a horizontal triangle ABC, AB = 20 m, BC = 30 m and angle ABC = 95°. (a) Calculate the length of AC. [2] (b) Calculate angle BAC. [2] (c) Find the shortest distance from B to AC. [2] (d) A vertical flagpole of height 12 m stands at A. A person walks along BC. Find the greatest angle of elevation of the top of the flagpole from a point on BC. [3]

Three points P, Q, R lie on horizontal ground. Q is due east of P with PQ = 60 m. The bearing of R from P is 45° and the bearing of R from Q is 315°. (a) Find angle QPR, angle PQR and angle PRQ. [2] (b) Find the distance QR. [3] (c) Find the area of triangle PQR and the shortest distance from R to PQ. [2]

A sector OAB has centre O and radius 15 cm. Angle AOB = 1.2 radians. M is the midpoint of OB. A line from A to M divides the sector into two regions. (a) Find the length of arc AB. [1] (b) Find the area of sector OAB. [2] (c) Find the length of AM. [2] (d) Find the area of the smaller region (bounded by arc AB, the line AM, and part of OB). [3]