Question

Solve for x. Round your awnser to the nearest tenth.

Answer 1

We are given a right triangle and we have to find the length of one of its sides. It will be useful to remember the definition of the tangent of an angle inside a right triangle. For an angle α<90° in a right triangle we have:

`\tan \alpha=\frac{\text{opposite side}}{\text{adjacent side}}`

If α is the 26° angle in the image then its opposite side is 11 and its adjacent side is x. Then we get:

`\tan 26^(\circ)=(11)/(x)`

We can multiply both sides of this equation by x:

`\begin{gathered} \tan 26^(\circ)\cdot x=(11)/(x)\cdot x \\ \tan 26^(\circ)\cdot x=11 \end{gathered}`

And we divide both sides by tan(26°):

`\begin{gathered} (\tan 26^(\circ)\cdot x)/(\tan 26^(\circ))=(11)/(\tan 26^(\circ)) \\ x=(11)/(\tan26^(\circ))=22.6 \end{gathered}`

Then the answer is 22.6.