Question

let length of longest side of right angle triangle is cos 48 degree if length of second side sin12 degrees


then length of third side is​

Answer 1

Answer:

Length of the third side is $\sqrt{\frac{\sqrt{5}+1}{8}}$

Step-by-step explanation:

Concept used:

Pythagors theorem:

In a right angled square on the hypotenuse is equal to sum of the squares on the other two sides.

$cos(A+B).cos(A-B)=cos^2A-sin^2B$

$cos36=\frac{\sqrt{5}+1}{4}$

Given:

hypotenuse = cos48

other side = sin12

Let the length of the third side be x

By pythagoras theorem,

$sin^212+x^2=cos^248$

$x^2=cos^248-sin^212$

$x^2=cos(48+12).cos(48-12)$

$x^2=cos60.cos36$

$x^2=\frac{1}{2}.(\frac{\sqrt{5}+1}{4})$

$x^2=\frac{\sqrt{5}+1}{8}$

$x=\sqrt{\frac{\sqrt{5}+1}{8}}$