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Basic Trigonometry Revision Notes π¬π’π§ π = πππ ππ¨π¬ π = πππ ππ π πππ§ π = πππ πππ ππ π x = angle hyp = hypotenuse(side opposite to the right angle) opp = opposite(side opposite to the non-right angle given in the question or opposite to the angle you are trying to find). adj = adjacent(side next to the non-right angle given in the question or opposite to the angle you are trying to find). Using Basic Trigonometry to find the length of a missing side e.g. hyp opp 14.6cm a 37o adj Label the sides. Select the rule. To do this you need to look at what side you are trying to find. In this example it is the opposite side. You then need to see which other side you know the length of. In this example you know that the hypotenuse is 14.6cm. You need to select the rule that contains these two sides. For this example therefore you need to use β π¬π’π§ π = πππ πππ You now need to substitute the known values into the rule. π¬π’π§ ππ = π ππ. π Rearrange the equation to find a. π = ππ. π × πππππ π = π. ππππ(ππ π) Using Basic Trigonometry to find a missing angle e.g. hyp opp 12.2cm x 7.8cm adj Label the sides. Select the rule. To do this you need to look at what sides you know the length of. In this example you know that the adjacent is 7.8cm and hypotenuse is 12.2cm. You need to select the rule that contains these two sides. For this example therefore you need to use β ππ¨π¬ π = ππ π πππ You now need to substitute the known values into the rule. ππ¨π¬ π = π. π ππ. π Rearrange the equation to find x. π = ππ¨π¬βπ ( π. π ) ππ. π π = ππ. πππ (ππ π) Key Points ο· ο· ο· ο· ο· ο· Basic Trigonometry can only be used on right angle triangles. If the question does not contain a right angle triangle, then you cannot use Basic Trigonometry to answer it! Basic Trigonometry can be used to find a missing side if you are given another side and at least one of the angles. Basic Trigonometry can also be used to find a missing angle if you are given at least two of the sides. Remember if you are finding a missing side and are given the other two sides, you should use Pythagorasβ Theorem to find the answer. Donβt forget to include units on your answer. Be careful when using your calculator. Make sure you enter the values in the correct order depending on your calculator. Exam Questions Q1. Calculate the value of x. Give your answer correct to 3 significant figures. ....................................................................................................................................... (Total for Question is 3 marks) Q2. Diagram NOT accurately drawn LMN is a right-angled triangle. MN = 9.6 cm. LM = 6.4 cm. Calculate the size of the angle marked x°. Give your answer correct to 1 decimal place. . . . . . . . . . . . . . . . . . . . . . .° (Total for Question is 3 marks) Q3. ABCD is a parallelogram. DC = 5 cm Angle ADB = 36° Calculate the length of AD. Give your answer correct to 3 significant figures. ....................................................................................................................................... (Total for Question is 4 marks) Q4. * The diagram shows a ladder leaning against a vertical wall. The ladder stands on horizontal ground. The length of the ladder is 6 m. The bottom of the ladder is 2.25 m from the bottom of the wall. A ladder is safe to use when the angle marked y is about 75°. Is the ladder safe to use? You must show all your working. (Total for Question is 3 marks) Past Paper Question Mock Exam Question
