 Trigonometry Sin, Cosine, Tan    Back to Trigonometry Units

Trigonometry is a branch of mathematics that means "measurement of, with and by means of triangles".

Astronomers as early as 150 BC developed the study of trigonometry.  By about 1500 AD the trig. ratios (sine, cosine and tangent) were established.  Once again, right-angled triangles, as in Pythagoras' Theorem,  are important when making calculations with the trig ratios.  Example

 The Navigator's Problem A ship travels 10 km on a course heading 50ş east of north. How far north,  and how far east has the ship travelled at this point?   Have a Go

Problem 1

The base of the right-angled triangle shown is 5 cm in length,  and the angle A is 60°.
Calculate the altitude BC.  Problem 2

Use Pythagoras' theorem to find the missing sides of these right-angled triangles.  Use these triangles to complete the following table.

 30° 45° 60° sin cos tan  Practice Questions

 Question 1A railway is inclined at an angle of 1° to the horizontal.  Find the vertical height climbed when a train travels 1 km up the hill.   answer The train will climb 17.45 m vertically. Question 2Find  "a" in the following triangles (leave your answers in surd form):  Use the table in Practice Question 2. Click to see Answer Question 3The foot of a ladder is 1.5 m from  a vertical wall.  The ladder makes an angle of 68° with the horizontal.  How far up the wall does the ladder reach? answer 3.7m Question 4The string of a kite is 120 m long and makes an angle of 70° with the horizontal.  What is the height of the kite? answer approx 112.8 m  Solution 1 back to Have a Go

Solution 2  30° 45° 60° sin   cos   tan 1 back to Have a Go 