Question

If tan x =5/12, then find sec x.

Answer 1

Hello!

$\bf{tan \:x} = \dfrac{5}{12} = \dfrac{\sf P}{\sf B}$

Now,

$\sf H^{2} = \sf P^{2} + \sf H^{2} \\ \\ \implies \sf H^{2} = (5)^{2} + (12)^{2} \\ \\ \implies \sf H^{2} = 25 + 144 \\ \\ \implies \sf H^{2} = 169 \\ \\ \implies \sf H = \sqrt{169} \implies \bf{H = 13}$

Then,

$\bf{sec\:x} = \dfrac{\sf H}{\sf B} \implies \boxed{\red{\bf{\dfrac{13}{12}}}}$

Cheers!

Answer 2

Answer:

sec x =13/12

Step-by-step explanation:

We are given the value of tan x=5/12 and we have to calculate the value of sec x.

Let us assume a right-angled triangle whose base angle is x.

Now, tan x= (Perpendicular / Base) =5/12

Hence, the perpendicular of the triangle is 5 units and the base is 12 units.

Hence, the hypotenuse of the triangle is given by $\sqrt{5^{2}+12^{2}  } =13$.

Now, sec x= (Hypotenuse / Base) =13/12 (Answer)