WASSCE SHS
In a right angled triangle, sine, cosine and tangent compare two sides. The right name depends on which sides the question gave you.
Label the sides from the angle you are using, not from the page. The hypotenuse is opposite the right angle and is the longest side. The opposite side is across from your angle. The adjacent side is the other side that touches your angle. Sine is opposite over hypotenuse. Cosine is adjacent over hypotenuse. Tangent is opposite over adjacent. A memory sentence is fine if it gives you the right ratio. Write the ratio before you calculate.
If you know two sides you can find a third by Pythagoras: the square of the hypotenuse equals the sum of the squares of the other two sides. Check that the triangle is right angled before you use these ratios. They do not apply to an acute triangle that has no right angle, until you drop a perpendicular and create one. Give angles in degrees when the question is in degrees, and round only at the end, to the place the question asks for.
The ratio is a mark, the substitution is a mark, and the value is a mark. Naming the wrong ratio is a method error. Opposite and adjacent swap when you move to the other acute angle, so label the angle on the diagram. A length must be positive. If the question asks for an angle, the answer is in degrees, not a ratio left unfinished.
These are practice questions in the style of the paper, with a model answer and a mark scheme. They are not a promise of what your paper will ask.
3 marks
In a right angled triangle the side opposite angle θ is 8 cm and the hypotenuse is 17 cm.
(a) Find sin θ. (1 mark)
(b) The third side is 15 cm. Find cos θ and tan θ. (2 marks)
(a) sin θ = 8/17.
(b) cos θ = 15/17. tan θ = 8/15.
2 marks
A right angled triangle has shorter sides 5 cm and 12 cm. Find the hypotenuse. (2 marks)
Hypotenuse = square root of (5² + 12²) = square root of (25 + 144) = square root of 169 = 13 cm.
2 marks
Explain why the sine of an angle in a right angled triangle cannot be greater than 1. (2 marks)
Sine is opposite divided by hypotenuse. The hypotenuse is the longest side, so the opposite is shorter than or equal to it, and the ratio cannot exceed 1.
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
Practise Core Mathematics freeFrom the sides you have, relative to the angle. Opposite and hypotenuse: sine. Adjacent and hypotenuse: cosine. Opposite and adjacent: tangent. Label the angle before you pick the ratio.
In a right angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides. It finds a side, not an angle. The trigonometric ratios find an angle, or a side when an angle is known. All WASSCE Core Mathematics past questions