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FINDING AN UNKNOWN SIDE
REMEMBER: Pythagoras’ Theorem is used to find an unknown side in a right angled
triangle when the other two sides are known.
Trigonometry is used when only one side and one of the acute angles is
known.
TYPE 1: Unknown Side as the numerator in the trig equation.(MULTIPLY)
1) Find x in these triangles correct to 2 decimal places.
b)
a)
7.6 m
x
x
59
31
5m
2) A flagpole has a guy rope from the top of the pole to a point on the
ground 12 m from the base of the pole. If the rope makes an angle of 36
with the ground, find the height of the pole.
When the unknown side is the numerator in the equation we multiply the
number by tan 
TYPE 2: Unknown side as the denominator in the equation. (DIVIDE)
b)
a)
49
4m
d
25
x
8.6 m
c) A ship out at sea observes a lighthouse on the top of a 70 m cliff at an
angle of 3. How far out at sea is the ship (to the nearest metre)?
70 m
3
When the unknown is on the bottom of the fraction in the equation we
divide the number by tan 
REMEMBER: Unknown on the TOP of the fraction , MULTIPLY the
number by tan 
Unknown on the BOTTOM of the fraction, DIVIDE the
number by tan 