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Mathematics

From the figure (1) given below, find the value of sec θ.

From the figure, find the value of sec θ. Trigonometrical Ratios, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Trigonometrical Ratios

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Answer

From figure,

⇒ BD = BC - CD = 21 - 5 = 16.

In △ADC,

⇒ AC2 = AD2 + DC2 [By pythagoras theorem]

⇒ AD2 = AC2 - DC2

⇒ AD2 = 132 - 52

⇒ AD2 = 169 - 25

⇒ AD2 = 144

⇒ AD = 144\sqrt{144}

⇒ AD = 12.

In △ABD,

⇒ AB2 = AD2 + BD2 [By pythagoras theorem]

⇒ AB2 = 122 + 162

⇒ AB2 = 144 + 256

⇒ AB2 = 400

⇒ AB = 400\sqrt{400}

⇒ AB = 20.

By formula,

sec θ = HypotenuseBase\dfrac{\text{Hypotenuse}}{\text{Base}}

= ABBD=2016=54\dfrac{AB}{BD} = \dfrac{20}{16} = \dfrac{5}{4}.

Hence, sec θ = 54\dfrac{5}{4}.

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