///Mixed Sine Cos Rules
Mixed Sine Cos Rules2018-07-05T15:50:02+10:00

Maths Made Easy Forums Standard Trigonometry Mixed Sine Cos Rules

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    g_trig_0029Use the diagram to find: 

    a. The length of XY. 

    b. The length of YZ.

    a. $$\frac{YZ}{\sin40^{\circ}}=\frac{120}{\sin18^{\circ}}$$ $$YZ=\frac{120\sin40^{\circ}}{\sin18^{\circ}}$$

    YZ = 249.6m

    g_trig_0030b. $$\cos58^{\circ}=\frac{WY}{249.6}$$

    WY =249.6 × cos 58°

    WY = 132.3m

    XW = XY + WY

    = 120 + 132.3

    = 252.3

  • AdminAdmin

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    g_trig_0010Which trigonometric formula would be the most useful in calculating the length of side YZ? 

    a. A = ½absin C 

    b. c2 = a2 + b2 – 2ab cos C 

    c. $$\cos C=\frac{a^2+b^2-c^2}{2ab}$$

    d. $$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$

    Option A will find the area, which is not what we are after

    Option B is the cos rule looking for a side, which requires two sides and the included angle, and for you to be looking for the side opposite the angle, which we do not have here

    Option C is the cos rule looking for an angle, and since we are looking for a side, this is no help

    Option D is the correct rule, as it is the sin rule, which requires pairs of angles/sides. the 19° is opposite YZ and the 131° is opposite the 15m

    ∴ D

  • AdminAdmin

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    g_trig_0031Use the diagram to find: 
    a. The length of BD, correct to 1 decimal place, 
    b. The size of ∠DBC, correct to the nearest degree.

     

    a. BD2 = 182 + 35.72 – 2 × 18 × 35.7 × cos 100°
    BD2 = 1821.66
    BD = 42.7

    b. $$\frac{\sin B}{41.5}=\frac{\sin 80^{\circ}}{42.7}$$

    $$\sin B=\frac{41.5\sin 80^{\circ}}{42.7}$$

    B = 73°

  • AdminAdmin

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    g_trig_0012ABCD is a quadrilateral in which AB = 14cm, BC = 10cm, AD = 17.5cm, ∠A = 50° and ∠C = 55°.
    a. Find BD.
    b. Find ∠BDC.

    g_trig_0013a. BD2 =  142 + 17.52 – 2 × 17.5 × 14 × cos 50º
    BD2 = 187.2840713
    BD = 13.69cm

     

    b. $$\frac{\sin D}{10} = \frac{\sin 55}{13.69}$$

    $$\sin D = 10\times\frac{\sin 55}{13.69}$$

    sin D = 0.598

    D = 37°

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