A rectangle is 48 cm long and 14 cm wide. If the diagonal makes an angle θ with the longer side, then what is (sec θ + cosec θ) equal to?

Given:

A rectangle is 48 cm long and 14 cm wide

Formula Used:

sec θ = Hypotenus/Base

cosec θ = Hypotenus/Perpendicula

Pythagorus theorem

(Hypotenus)² = (Perpendicular)² +(Base)²

Calculation:

Triangle ABC is right angle triangle:

Hypotenuse = AC = x = \(\sqrt {{{48}^2} + {{14}^2}} = \sqrt {2304 + 196} = \sqrt {2500}\) = 50

Here,

Sec θ = AC/AB = 50/48

Cosec θ = AC/BC = 50/14

Hence,

(sec θ + cosec θ) = (50/48) + (50/14) = 1550/336 = 775/168 

∴ The value sec θ + cosec θ of is 775/168