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

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

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

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

$\tan x=\frac{6}{4}$

$\tan x=\frac{3}{2}$

$x=\tan ^{-1}(\frac{3}{2})$

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

$x=56.30$

$x\approx56^o$

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

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