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Right-Angled Triangles (Pythagoras & Trigonometry) (Cambridge (CIE) IGCSE Maths)

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  • FrontPythagoras Theorem

    What is the hypotenuse?

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  • What is the hypotenuse?

    The hypotenuse is the longest side in a right-angled triangle.

    It is located opposite the right angle.

  • State the equation, in terms of a, b, and c, for Pythagoras' theorem, where c is the length of the hypotenuse.

    The equation for Pythagoras' theorem is a squared plus b squared equals c squared

    Where:

    • a and b are the lengths of the two shorter sides

    • c is the length of the hypotenuse

  • True or False?

    Pythagoras' theorem applies to equilateral triangles.

    False.

    Pythagoras' theorem can only be used on right-angled triangles.

    An equilateral triangle contains no right angles. However an isosceles or scalene triangle may also be a right-angled triangle.

  • True or False?

    To find the length of the hypotenuse, you add inside the square root.

    True.

    To find the length of the hypotenuse, you add inside the square root using c equals square root of a squared plus b squared end root

  • What is the equation to find the length of one of the shorter sides in a right-angled triangle?

    To find the length of one of the shorter sides in a right-angled triangle, use the equation a equals square root of c squared minus b squared end root or b equals square root of c squared minus a squared end root.

  • What does SOHCAHTOA stand for?

    SOHCAHTOA is a mnemonic to help you remember the different trigonometric ratios.

    It stands for:

    • Sin = Opposite ÷ Hypotenuse

    • Cos = Adjacent ÷ Hypotenuse

    • Tan = Opposite ÷ Adjacent

  • State the SOHCAHTOA equation for sine.

    The SOHCAHTOA equation for sine is sin open parentheses theta close parentheses equals Opposite over Hypotenuse.

  • State the SOHCAHTOA equation for cosine.

    The SOHCAHTOA equation for cosine is cos open parentheses theta close parentheses equals Adjacent over Hypotenuse.

  • State the SOHCAHTOA equation for tangent.

    The SOHCAHTOA equation for tangent is tan open parentheses theta close parentheses equals Opposite over Adjacent.

  • What type of triangles can SOHCAHTOA be used on?

    SOHCAHTOA can only be used on right-angled triangles.

  • What does the inverse trigonometric function do, e.g. sin to the power of negative 1 end exponent?

    The inverse trigonometric function is used to find missing angles when two sides of a right-angled triangle are known.

    E.g. theta equals sin to the power of negative 1 end exponent open parentheses Opposite over Hypotenuse close parentheses.

  • What labels are given to the sides of a triangle when using SOHCAHTOA?

    The three sides are labelled the Hypotenuse (the side opposite the right-angle), the Adjacent (the side next to the angle in question) and the Opposite (the side opposite the angle in question).

    A right-angled triangle with the sides labelled hypotenuse, adjacent and opposite with regard to the angle θ.

  • What is the angle of elevation?

    The angle of elevation is the angle between the horizontal and the line of sight when looking up at an object.

    A person looking up at a bird. The angle of elevation is marked between the horizontal and the line of sight.

  • What is the angle of depression?

    The angle of depression is the angle between the horizontal and the line of sight when looking down at an object.

    A person looking down at a boat. The angle of depression is marked between the horizontal and the line of sight.

  • Which trigonometric ratio is often used in problems involving angles of elevation and depression?

    The trigonometric ratio that is often used in real-life scenarios with angles of elevation and depression is the tangent ratio.

    This is because real-life questions are often concerned with the height of an object (the 'opposite' side) and the horizontal distance from an object (the 'adjacent' side).

  • What is the exact value of the cosine of 0º?

    The exact value of the cosine of 0º is 1.

    cos open parentheses 0 close parentheses equals 1.

  • What is the exact value of the sine of 90º?

    The exact value of the sine of 90º is 1.

    sin open parentheses 90 close parentheses equals 1.

  • What is the exact value of the tangent of 0º?

    The exact value of the tangent of 0º is 0.

    tan open parentheses 0 close parentheses equals 0.

  • What is the exact value of the tangent of 45º?

    The exact value of the tangent of 45º is 1.

    tan open parentheses 45 close parentheses equals 1.

  • What is the exact value of both the cosine and the sine of 45º?

    The exact value of both the cosine and the sine of 45º is fraction numerator square root of 2 over denominator 2 end fraction.

    This can also be written as fraction numerator 1 over denominator square root of 2 end fraction.

    cos open parentheses 45 close parentheses equals sin open parentheses 45 close parentheses equals fraction numerator square root of 2 over denominator 2 end fraction equals fraction numerator 1 over denominator square root of 2 end fraction.

  • The sine of which angle (between 0º and 90º) has an exact value of 1 half?

    The sine of 30º has an exact value of 1 half.

    sin open parentheses 30 close parentheses equals 1 half.

  • What is the exact value of the cosine of 90º?

    The exact value of the cosine of 90º is 0.

    cos open parentheses 90 close parentheses equals 0.

  • The tangent of which angle (between 0º and 90º) has an exact value of fraction numerator square root of 3 over denominator 3 end fraction?

    The tangent of 30º has an exact value of fraction numerator square root of 3 over denominator 3 end fraction.

    tan open parentheses 30 close parentheses equals fraction numerator square root of 3 over denominator 3 end fraction.

  • What is the exact value of the tangent of 60º?

    The exact value of the tangent of 60º is square root of 3.

    tan open parentheses 60 close parentheses equals square root of 3.

  • What is the exact value of the cosine of 60º?

    The exact value of the cosine of 60º is 1 half.

    cos open parentheses 60 close parentheses equals 1 half.

  • What is the exact value of the sine of 0º?

    The exact value of the sine of 0º is 0.

    sin open parentheses 0 close parentheses equals 0.

  • For which angle (between 0º and 90º) is the tangent of it undefined?

    The tangent of the angle 90º is undefined.

  • What is the exact value of both the cosine of 30º and the sine of 60º?

    The exact value of both the cosine of 30º and the sine of 60º is fraction numerator square root of 3 over denominator 2 end fraction.

    cos open parentheses 30 close parentheses equals sin open parentheses 60 close parentheses equals fraction numerator square root of 3 over denominator 2 end fraction.

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