Question

Trigonometric Ratios Express the length x in terms of the trigonometric ratios of $\theta$.

Short answer

Therefore the expression of x from the given triangle in terms of $\theta$is given by $\mathit{x}\mathbf{=}\mathbf{10}\mathit{s}\mathit{i}\mathit{n}\mathit{\theta }\mathit{t}\mathit{a}\mathit{n}\mathit{\theta }$.

Step-by-step solution

Step 1. Given information.

The dimensions of the given figure 10,$\theta$

Step 2. Applying the trigonometric ratios in the right-angled triangles

Considering the below figure,

Substituting the known values of $\theta$and the adjacent side in the above trigonometric ratio formulae, we get,

$\begin{array}{c}\tan \theta =\frac{y}{10}\\ \Rightarrow y=10\tan \theta \end{array}$

Step3. Finding the value of x

From the figure, we can observe from the lower triangle that,

$\begin{array}{c}\sin \theta =\frac{x}{y}\\ \Rightarrow x=y\sin \theta \\ \Rightarrow x=10\tan \theta \sin \theta \end{array}$