Solution of a Right Angled Triangle

Finding the solution of right angled triangle means to find the all six parameters of the triangle. In the following cases solution of a triangle can be found:

    If three elements of any triangle are known, then the remaining elements can be calculated.

    In a right-angled triangle, one element is known i.e. one right angle.

So a right-angled triangle can be solved if

    two sides of the triangle are given.

    one side and one acute angle are given.

Cosecant (cosec) of an angle: The ratio of the hypotenuse to the perpendicular is called the cosecant of the angle.

Cosine (cos) of an angle: The ratio of the base or adjacent side to the hypotenuse is called the cosine of the angle.

Cotangent (cot) of an angle: The ratio of the base to the perpendicular is called the cotangent of the angle.

Secant (sec) of an angle: The ratio of the hypotenuse to the base is called the secant of the angle.

Sine (sin) of an angle: The ratio of the perpendicular or opposite side to the hypotenuse is called the sine of the angle.

Tangent (tan) of an angle: The ratio of the perpendicular to the base is called the tangent of the angle.

Trigonometric ratio: The ratio between the lengths of a pair of two sides of a right-angled triangle is called trigonometric ratio.

Trigonometric Ratios of Complementary Angles: If the sum of two angles is 90°, then they are said to be complementary angles.

Sin (90° – ?) = cos ?

cos (90° – ?) = sin ?

tan (90° – ?) = cot ?

cosec (90° – ?) = sec ?

sec (90° – ?) = cosec?

cot (90° – ?) = tan ?

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  • Q1

    If cos9A= sinA and 9A

    Marks:2
    Answer:

    Since, cos9A = sinA, then

    cos9A = cos (90 - A)

    9A = 90 - A

    10A = 90
    A = 90/10
    = 9
    So, we have

    tan5A = tan5(9)

    = tan45
    =1

    View Answer
  • Q2

    If sin3A = cos (A – 26), where 3A is an acute angle, find the value of A.

    Marks:2
    Answer:

    Since, sin3A = cos (A – 26)
    cos (90
    - 3A) = cos (A – 26)
    90
    - 3A = A – 26
    90
    +26= A + 3A
    116
    = 4A

    This gives,

    A = 116/4

    = 29

    View Answer
  • Q3

    Evaluate: sin 13 - cos 87

    Marks:1
    Answer:

    sin 13 - con 87

    = cos (90- 13) - cos 87

    [Since, sin x = cos(90- x) ]

    = cos 87 - cos 87

    = 0

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  • Q4

    If tan A = cot B, prove that A + B = 90.

    Marks:1
    Answer:

    Given,tan A = cot B
    tan A = tan (90 − B) ( Since, tan (90 − x) = cot x )
    or, A = 90 − B
    or, A + B = 90

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  • Q5

    Show that:tan48 tan23 tan42 tan67 = 1

    Marks:1
    Answer:

    tan 48 tan 23 tan 42 tan 67
    = tan (90 − 42) tan (90 − 67) tan 42 tan 67
    = cot 42 cot 67 tan 42 tan 67
    = (cot 42 tan 42) (cot 67 tan 67)
    = (1) (1)
    = 1

    View Answer