Question 1 Foundation
A tangent touches a circle at , and is the centre. What is the size of angle , where is a point on the tangent?
Answer.
A tangent is perpendicular to the radius drawn to the point of contact — always exactly a right angle.
Geometry and Trigonometry II
Original questions written at exam standard. Work each one before you open the solution.
Difficulty
Question 2 Foundation
Write the bearing of due south-east as a three-figure bearing.
Answer.
South-east is halfway between east () and south (), measured clockwise from north.
Question 3 Standard
The angle at the centre of a circle standing on an arc is . Find the angle at the circumference on the same arc.
Answer.
The angle at the centre is twice the angle at the circumference, so halve it.
Question 4 Standard
A ladder leans against a wall, reaching 5 m up, with its foot 2 m from the wall. Find the angle of elevation of the top of the ladder from its foot.
Answer. (1 d.p.)
, so .
Question 5 Stretch
In triangle , cm, cm and angle . Find .
Answer. cm (3 s.f.)
Two sides and the included angle, so use the cosine rule: , and cm.
Question 6 Stretch
The bearing of from is . Find the bearing of from .
Answer.
The bearing is or more, so subtract: , written with three figures as .