Maths-
General
Easy

Question


In the right triangle above, sin theta equals 2 over 5 . If  AC = square root of n, what is the value of n?

The correct answer is: 84


    Step by step explanation:
    Given:
    In straight triangle ABC,
    Sin invisible function application theta equals 2 over 5
    AB = 10,
    AC = square root of n
    Step 1:
    We know that, in right angle triangle
    sin theta equals fraction numerator text  Perpendicular  end text over denominator text  Hypotenus  end text end fraction
    So, according to given information,
    sin theta equals BC over AB
    Step 2:
    Put value of sin theta equals 2 over 5
    not stretchy rightwards double arrow 2 over 5 equals fraction numerator B C over denominator 10 end fraction
    Step 3:
    Now, cross multiply each other
    not stretchy rightwards double arrow B C equals fraction numerator 10 cross times 2 over denominator 5 end fraction
    ⇒ BC = 4
    Step 2:
    In straight triangle ABC,
    Apply pythagorus theorem,
    ⇒ AC2 + BC= AB2
    not stretchy rightwards double arrow left parenthesis square root of n right parenthesis squared plus 4 squared equals 10 squared open curly brackets because left parenthesis square root of a right parenthesis squared equals a close curly brackets
    ⇒ n + 16 = 100
    ⇒ n = 100 - 16
    n = 84

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