Question

Find the missing side lengths. Leave your answers as radicals in simplest form.

Answer 1

B x = 3, y= 3

Explanation:

Trigonometric ratios

`\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)`

where:

• 
  `\theta` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle
• H is the hypotenuse (the side opposite the right angle)

Given:

• 
  `\theta` = 45°
• O =
  `x`
• A =
  `y`
• H =
  `3√(2)`

`\implies \sin(45^(\circ))=(x)/(3√(2))`

`\implies x=3√(2)\sin(45^(\circ))`

`\implies x=3√(2) \cdot (√(2))/(2)`

`\implies x=(3√(2) √(2))/(2)`

`\implies x=(3 \cdot 2)/(2)=3`

`\implies \cos(45^(\circ))=(y)/(3√(2))`

`\implies y=3√(2)\cos(45^(\circ))`

`\implies y=3√(2) \cdot (√(2))/(2)`

`\implies y=(3√(2) √(2))/(2)`

`\implies y=(3 \cdot 2)/(2)=3`