Find the side indicated by the variable. Round to the nearest tenth.PLEASE HELP

Find the side indicated by the variable. Round to the nearest tenth.
PLEASE HELP


[tex]Find the side indicated by the variable. Round to the nearest tenth. PLEASE HELP[/tex]

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  1. QUESTION 1

    The given triangle is right triangle with an acute angle measuring [tex]53\degree[/tex].

    The length of the given side which is opposite to the [tex]53\degree[/tex] angle is 8 units.

    Recall that;

    [tex]\sin(53\degree)=\frac{Opposite}{Hypotenuse}[/tex]

    [tex]\Rightarrow \sin(53\degree)=\frac{8}{u}[/tex]

    [tex]\Rightarrow u=\frac{8}{\sin(53\degree)}[/tex]

    [tex]\Rightarrow u=10.017[/tex]

    [tex]\Rightarrow u=10.0[/tex] to the nearest tenth

    QUESTION 2

    The given right angle triangle has an acute angle measuring [tex]68\degree[/tex].

    The hypotenuse has length 11 units.

    [tex]c[/tex] is the length of the opposite side.

    We use the sine ratio again to obtain;

    [tex]\sin(68\degree)=\frac{c}{11}[/tex]

    [tex]c=11\sin(68\degree)[/tex]

    [tex]c=10.197[/tex]

    [tex]c=10.2[/tex] to the nearest tenth.

    QUESTION 3

    This time the right angle triangle has an acute angle of [tex]59\degree[/tex] and the side opposite this angle is 26 units,

    We again use the sine ratio to obtain;

    [tex]\sin(59\degree)=\frac{26}{k}[/tex]

    [tex]\Rightarrow k=\frac{26}{\sin(59\degree)}[/tex]

    [tex]\Rightarrow k=30.335[/tex]

    [tex]\Rightarrow k=30.3[/tex] to the nearest tenth,

    QUESTION 4

    The given right angle triangle has an acute angle measuring [tex]22\degree[/tex].

    The hypotenuse has length 5 units.

    [tex]a[/tex] is the length of the opposite side.

    We use the sine ratio again to obtain;

    [tex]\sin(22\degree)=\frac{a}{5}[/tex]

    [tex]a=5\sin(22\degree)[/tex]

    [tex]a=1.875[/tex]

    [tex]a=1.9[/tex] to the nearest tenth.

    QUESTION 5

    This time the given right angle triangle has an acute angle of [tex]47\degree[/tex] and the side opposite this angle has length 51 units.

    The side we want to find is adjacent to the given angle. We use the tangent ratio to obtain;

    [tex]\tan(47\degree)=\frac{51}{b}[/tex]

    [tex]b=\frac{51}{\tan(47\degree)}[/tex]

    [tex]b=47.558[/tex]

    [tex]b=47.6[/tex] to the nearest tent.

    QUESTION 6

    The given right angle triangle has an acute angle measuring [tex]49\degree[/tex].

    The hypotenuse has length 6 units.

    The side whose length we want to find is opposite to the given angle, we use the sine ratio to get;

    [tex]\sin(49\degree)=\frac{n}{6}[/tex]

    [tex]\Rightarrow n=6\sin(49\degree)[/tex]

    [tex]\Rightarrow n=4.528[/tex]

    [tex]n=4.5[/tex] to the nearest tenth.

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