Question

What is the exact length of HG in cms

Answer 1

Let's solve ~

The given triangle is a right angled triangle, therefore the rules of basic Trigonometry can be used here to find the solution.

Considering angle G, lets find sin 45°

`\qquad\displaystyle \tt \dashrightarrow \: \sin(45 \degree) = (opposite \:\: side)/(hypotenuse)`

[ sin 45° = 1/√2 ]

`\qquad\displaystyle \tt \dashrightarrow \: (1)/( √(2) ) = (b)/(x)`

`\qquad\displaystyle \tt \dashrightarrow \: x = b √(2) \: \: cm`

So, the side HG is b√2 cm long