SOHCAHTOA — Introduction
Grade 5What SOHCAHTOA means
SOHCAHTOA is a memory aid for the three trigonometric ratios that link sides and angles in right-angled triangles.
The hypotenuse is opposite the right angle. The opposite is the side facing the angle θ. The adjacent is the remaining side, next to angle θ.
Label the triangle first
Before touching a calculator, label the three sides relative to the angle you are working with. Opposite, Adjacent, Hypotenuse. Then choose the correct ratio — it is the one that involves the two sides (or the side and angle) you are dealing with.
Worked example — finding a side
Try this one
Past paper - 2023
Taylor designs a logo using isosceles triangles joined at a central point, P.
This is the start of Taylor’s design.
The completed design will have rotational symmetry, order 60 about point P
Each triangle has base, b, and height, h, measured in mm.
Calculate h when b = 40mm.
Give your answer correct to 1 decimal place.
(a)----------------------------mm [4]
This question uses trigonometry inside an isosceles triangle. Because the design has rotational symmetry of a certain order, you can find the angle at point P by dividing 360° by that order.
Ask yourself: 'If I drop a perpendicular from P to the base, what right-angled triangle is formed, and which trig ratio connects the half-base and the height?'
For example, if a design had order 4, the central angle would be 90°, giving a half-angle of 45° — you would then use tan(45°) = (half base) ÷ height.
