Question

How do I find the X and y value in this type of triangle?

Answer 1

The given triangle is a right-angled triangle

Recall that

`\tan \theta=\frac{Opposite\text{ side}}{\text{Adjacent side}}`

`Let\text{ }\theta=x,\text{ then Opposite side=6 and adjacent side =4.}`

`\text{Substitute known values in }\tan \theta=\frac{Opposite\text{ side}}{\text{Adjacent side}}\text{ as follows:}`

`\tan x=(6)/(4)`

`\tan x=(3)/(2)`

`x=\tan ^(-1)((3)/(2))`

`Substitute\tan ^(-1)((3)/(2))=56.30\text{ as follows:}`

`x=56.30`

`x\approx56^o`

Using the triangle sum property, we get

`90^o+x+y=180^0`

`x+y=180^0-90^o`

`x+y=90^o`

`Substitutex=56^o\text{ as follows:}`

`56^o+y=90^o`

`y=90^o-56^o`

`y=34^o`

Hence the values of x and y are

`x=56^o\text{ and }y=34^o`