Question

Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale. (image attached)thank you ! :)

Answer 1

The measure of an acute angle of a right triangle is given.

The length of the side adjacent to this angle is 11 and the length of the hypotenuse is x.

It is required to find the value of x.

Recall that the Cosine Ratio is given as:

`\cos\theta=\frac{\text{ Adjacent}}{\text{ Hypotenuse}}`

Substitute θ=24º, Adjacent=11, and Hypotenuse=x into the equation:

`\begin{gathered} \cos24^(\circ)=(11)/(x) \\ \Rightarrow x\cos24^(\circ)=11 \\ \text{ Divide both sides by }\cos24^(\circ): \\ \Rightarrow(x\cos24^(\circ))/(\cos24^(\circ))=(11)/(\cos24^(\circ)) \\ \Rightarrow x=(11)/(\cos24^(\circ))\approx12.0 \end{gathered}`

The value of x is about 12.0.