Mathematics
From the figure (1) given below, find the value of sec θ.
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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 =
⇒ AD = 12.
In △ABD,
⇒ AB2 = AD2 + BD2 [By pythagoras theorem]
⇒ AB2 = 122 + 162
⇒ AB2 = 144 + 256
⇒ AB2 = 400
⇒ AB =
⇒ AB = 20.
By formula,
sec θ =
= .
Hence, sec θ = .
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