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10 February, 06:12

To the nearest tenth of a degree, find the sizes of the acute angles in the 5-12-13 triangle and in the 9-12-15 triangle. This enables you to calculate the sizes of the angles in the 13 - 14-15 triangle. Show how to do it, then invent another example of this sort.

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  1. 10 February, 08:00
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    Step-by-step explanation:

    A triangle whose sides are 5-12-13 is a right angle triangle because the sides form a Pythagoras triple. This means that

    Hypotenuse² = opposite side² + adjacent side²

    If hypotenuse = 13,

    Opposite side = 12, then we can determine one acute angle by applying the sine trigonometric ratio

    Sin θ = opposite side/adjacent side

    Sin θ = 12/13 = 0.923

    θ = Sin^-1 (0.923) = 67.4°

    The other acute angle is

    90 - 67.4 = 22.6°

    For 9-12-15 triangle

    Sin θ = 12/15 = 0.8

    θ = Sin^-1 (0.8) = 53.1°

    The other acute angle is

    90 - 53.1 = 36.9°

    For 13 - 14-15 triangle,

    Sin θ = 14/15 = 0.933

    θ = Sin^-1 (0.933) = 68.9°

    The other acute angle is

    90 - 68.9 = 21.1°

    Another example would be 3-4-5

    Sin θ = 4/5 = 0.933

    θ = Sin^-1 (0.8) = 53.1°

    The other acute angle is

    90 - 53.1 = 36.9°
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