This order can spell the word ‘SOHCAHTOA’. Alternatively, the formulae can be memorised using the mnemonic Silly Old Harry Caught A Herring Trawling Off America
SOHCAHTOA is generally used to calculate the length of the ‘opposite’ or the ‘adjacent’, given the angle and the hypotenuse.
Opp = H sin u; Adj = H cos u
Angles can be described in degrees or radians, or in terms of inverse trigonometric functions; for example:
u = tan-1a
Opposite Adjacent b
SAMPLE PROBLEM 2A u
PYTHAGORAS OF SAMOS, C. 576—495 BC (GREEK) The ‘father of numbers’ is best known for the theorem which bears his name. He also founded the religious move- ment called Pythagoreanism.
(i) For a right-angled triangle of sides 7 m and 24 m as illustrated in Fig 2.5, calculate the length of the hypotenuse and the angle .
Hyp 7 24 Fig 2.5
(ii) For a right-angled triangle of angle 22.62 to the horizontal and hypotenuse 13 m as illustrated in Fig 2.6, calculate the lengths of the other two sides.
13 22.62
Fig 2.6 Adj
SAMPLE ANSWER 2A (i) Using Pythagoras:
H2 72 242 49 576 625 H 1625 25
The hypotenuse is 25 m in length. Using SOHCAHTOA:
tan 7 24 Q tan1 7
16.26° (ii) Using SOHCAHTOA:
sin 22.62° Opp 13 QOpp 13(sin 22.62°) 13(0.3846) 5
The other two sides of the triangle are 5 m and 12 m. cos 22.62° Adj
