Question

Pls help! Step by step

Answer 1

`x=6√(2)`

Explanation:

`\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(O)/(A)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

From inspection of the given right triangle:

• θ = 45°
• A = 6
• H = x

Substitute the given values into the cosine trigonometric ratio and solve for x:

`\implies \cos(45^(\circ))=(6)/(x)`

`\implies (√(2))/(2)=(6)/(x)`

`\implies x√(2)=6 \cdot 2`

`\implies x√(2)=12`

`\implies x=(12)/(√(2))`

`\implies x=(12)/(√(2))\cdot (√(2))/(√(2))`

`\implies x=(12√(2))/(2)`

`\implies x=6√(2)`

Answer 2

x = 6
`√(2)`

Explanation:

using the cosine ratio in the right triangle and the exact value

cos45° =
`(1)/(√(2) )` , then

cos45° =
`(adjacent)/(hypotenuse)` =
`(6)/(x)` =
`(1)/(√(2) )` ( cross- multiply )

x = 6
`√(2)`

This is the exact value for x. It may be rounded if you wish