Maths-
General
Easy

Question

Triangle PQR has right angle Q. If sin R = 4 over 5, what is the value of tan P?

The correct answer is: 0.6


    ○        Triangle with one angle of 90॰ is called right angle triangle.
    ○        Side opposite to 90॰ is called Hypotenus.
    ○        Pythagoras theorem, according to which (side)2 +  (side)2 = (hypotenus)2
    ○        In right angled triangle,
    Sin invisible function application theta equals fraction numerator text  Perpendicular  end text over denominator text  Hypotenus  end text end fraction
    Cos invisible function application theta equals fraction numerator text  Base  end text over denominator text  Hypotenus  end text end fraction
    Tan invisible function application theta equals fraction numerator text  Perpendicular  end text over denominator text  Base  end text end fraction
    • Step by step explanation:
    ○        Given:

    In △PQR,
    sin invisible function application R equals 4 over 5
    ○        Step 1:
    We know that, in right angle triangle
    According to pythagoras theorem,
    PQ2 + RQ2 = PR2
    ∴ 42 +RQ2 = 52
    16 +RQ2 = 25
    RQ2 = 25 - 16
    RQ2 = 9
    RQ =square root of 9
    RQ = 3
    ○        Step 2:
    ○        We know that,
    Tan invisible function application theta equals fraction numerator text  Perpendicular  end text over denominator text  Base  end text end fraction
    not stretchy rightwards double arrow Tan invisible function application straight P equals fraction numerator R Q over denominator P Q end fraction
    not stretchy rightwards double arrow Tan invisible function application straight P equals 3 over 5
    Tan invisible function application P equals 3 over 5
    • Final Answer:
    Hence, the Tan invisible function application P equals 3 over 5 = 0.6

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