Question

Find the value of sec60 geometrically

Answer 1

Draw an equilateral triangle with side lengths 2.
Bisect it via the perpendicular bisectors of one of its sides.
You now have two congruent right-angled triangles with a 60 degree angle in them.
The hypotenuse will be 2, the bisected side will be 1, and we can work out the other side to be sqrt(3) using pythagoras's theorem.
The sec function is 1 / cos, so it will be hypotenuse over adjacent.
The adjacent side will be the side length 1, and the hypotenuse is still 2.
Thus sec(60) = 2 / 1 = 2.


Hope this will help you..

Answer 2

Draw an equilateral triangle with side lengths 2.

Bisect it via the perpendicular bisectors of one of its sides.

You now have two congruent right-angled triangles with a 60 degree angle in them.

The hypotenuse will be 2, the bisected side will be 1, and we can work out the other side to be sqrt(3) using pythagoras's theorem.

The sec function is 1 / cos, so it will be hypotenuse over adjacent.

The adjacent side will be the side length 1, and the hypotenuse is still 2.

Thus sec(60) = 2 / 1 = 2.