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θ
OPPOSITE
HY
PO
TE
NU
SE
A D J A C E N T
The three trigonometric ratios
Sin θ =Opposite
Hypotenuse S O H
Cos θ =Adjacent
Hypotenuse C A H
Tan θ =OppositeAdjacent T O A
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Finding side lengths
If we are given one side and one acute angle in a right-angled triangle, we can use one of the three trigonometric ratios to find the lengths of other sides.
56°
x12 cm
To find the length of the side oppositethe angle, given the hypotenuse, use:
sin θ =opposite
hypotenuse
sin 56° =x
12
x = 12 × sin 56°
= 9.95 cm
Find x to 2 decimal places.
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Finding side lengths
A 5 m ladder is resting against a wall. It makes an angle of 70° with the ground.
5 m
70°x
To find the length of the side adjacentto the angle, given the hypotenuse, use:
cos θ =adjacent
hypotenuse
cos 70° =x5
x = 5 × cos 70°= 1.71 m (to 2 d.p.)
What is the distance between the base of the ladder and the wall?
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Finding angles