Introduction to Trigonometry - Worksheets, Questions and Revision

18 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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KS3 · Geometry and Measures

KS3.M-G15 Introduction to Trigonometry

AQA KS3.M-G15 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A right-angled triangle has angle A = 90 degrees, angle B = 30 degrees and hypotenuse 10 cm. Write down the lengths of the opposite and adjacent sides to angle B in words.
(a)Name the side opposite angle B.(1)
(b)Name the side adjacent to angle B (but not the hypotenuse).(1)
2
Write down the trigonometric ratio you would use to find the length of the opposite side given the angle and hypotenuse. Give the ratio name and the formula in words.
(a)Name the ratio.(1)
(b)Write the formula in words.(1)
3
Calculate the length of the opposite side in question 1 using sine. Give your answer to 1 decimal place. (Angle B = 30 degrees, hypotenuse = 10 cm.)
(a)Calculate opposite = sin(30) x hypotenuse.(2)
4
A right-angled triangle has one acute angle 40 degrees. The side adjacent to the 40 degree angle measures 6 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.
(a)Find hypotenuse using cosine: cos(40) = adjacent/hypotenuse.(3)
5
A student uses tan to find a length. In a right-angled triangle angle C = 50 degrees and the side adjacent to C is 4 m. Find the length of the opposite side, giving your answer to 1 decimal place.
(a)Use tan(50) = opposite / adjacent to find opposite.(3)
6
In a right-angled triangle the hypotenuse is 13 cm and one acute angle is 67 degrees. Which trig ratio would you use to find the side adjacent to the 67 degree angle? State the ratio name and formula.
(a)Name the ratio.(1)
(b)Write the formula in words.(1)
7
A ladder leans against a wall making an angle of 75 degrees with the ground. The foot of the ladder is 2.0 m from the wall. Find the length of the ladder to 1 decimal place.
(a)Use cos(75) = adjacent / hypotenuse to find ladder length.(3)
8
A right-angled triangle has sides 9 cm (opposite to angle X), 12 cm (adjacent to X) and hypotenuse 15 cm.
(a) Verify which trig ratio equals 9/15 for angle X.
(b) Use that ratio to find angle X to the nearest degree.
(a)State the trig ratio equal to 9/15.(1)
(b)Find angle X using sin^{-1}(9/15).(3)
9
Find the missing side in the right-angled triangle. Angle Y = 23 degrees, hypotenuse = 14 cm. Find the adjacent side to angle Y, to 1 decimal place.
(a)Use cos(23) = adjacent / 14.(3)
10
A student tries to use sin instead of cos to find the adjacent side in question 9. Explain briefly why sin(23) x 14 is incorrect for the adjacent side.
(a)Give a brief reason.(2)
11
Find angle Z in the right-angled triangle where opposite = 7 cm and adjacent = 24 cm. Give your answer to the nearest degree.
(a)Use tan to find the angle: tan(Z) = opposite / adjacent.(2)
12
A right-angled triangle has one side 8 m and another side 15 m. Show that the triangle could have hypotenuse 17 m, then find one acute angle to the nearest degree using trigonometry.
(a)Show that 82 + 152 = 172.(1)
(b)Find the angle opposite the side of length 8 m, to the nearest degree.(2)
13
A right-angled triangle has an acute angle of 31 degrees and the opposite side is 5 cm. Find the hypotenuse to 1 decimal place.
(a)Use sin(31) = opposite/hypotenuse to find the hypotenuse.(3)
14
A right-angled triangle has sides 10 cm (adjacent to angle A) and 24 cm (hypotenuse). Find angle A to the nearest degree.
(a)Use cos to find angle A: cos(A) = 10 / 24.(2)
15
A right-angled triangle has angle P = 58 degrees and an opposite side 9 cm. Find the adjacent side, giving your answer to 1 decimal place.
(a)Use tan(58) = opposite / adjacent and rearrange to find adjacent.(3)
16
A triangular roof has a right-angled cross section. The roof rises 3 m over a horizontal run of 5 m. Find the angle of elevation of the roof to the nearest degree.
(a)Use tan(θ) = opposite / adjacent = 3 / 5.(2)
17
Stretch: A right-angled triangle has hypotenuse 20 cm. One acute angle is twice the other. Find the two acute angles to the nearest degree.
(a)Let the smaller angle be x degrees. Then the other is 2x. Use sin or cos to set up an equation and find x.(2)
18
Stretch: A right-angled triangle has one acute angle 22 degrees and the side adjacent to it measures 11 cm. The opposite side is increased by 20% while the adjacent side stays the same. Calculate the new angle to the nearest degree.
(a)Find original opposite, increase it by 20% then find new angle using tan^{-1}.(2)
Mark scheme · KS3.M-G15 Introduction to Trigonometry

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18