3.3 Applications of trigonometryIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

\sin\theta, \cos\theta, \tan\theta in a right-angled triangle?
State Pythagoras' theorem.
Angle of elevation?
Angle of depression?
How are the angle of depression from a cliff and the angle of elevation from the boat related?
How is a bearing measured?
The bearing of B from A is 125^\circ. Bearing of A from B?
15 km on a bearing of 070^\circ: eastward and northward distances?
State the sine rule.
State the cosine rule for a side.
State the cosine rule for an angle.
Area of a triangle from two sides and the included angle?
When do you use the cosine rule rather than the sine rule?

Exam questions on 3.3 Applications of trigonometry

A vertical tower stands on level ground. A surveyor at point $A$ , 40 m from the base of the tower, measures the angle of elevation of the top of the tower as $35^\circ$ . Use your GDC where needed.
A flagpole of height 5 m stands on top of the tower. Find the angle of elevation of the top of the flagpole from $A$ .2 marks
A ship leaves port $P$ and sails 15 km on a bearing of $070^\circ$ to a point $Q$ .
Find the bearing of $P$ from $Q$ .2 marks
Two lifeguard towers $A$ and $B$ stand on a straight, level beach, 200 m apart. A swimmer is at a point $S$ in the sea. From $A$ , $S\hat{A}B=52^\circ$ and from $B$ , $S\hat{B}A=71^\circ$ . Use your GDC where needed.
Find the size of $A\hat{S}B$ and hence find the distance $AS$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).