Question

Trigonometric Ratios

Express $\mathit{x}$and $\mathit{y}$in terms of trigonometric ratios of $\mathit{\theta }$

Short answer

The values are$\mathit{x}\mathbf{=}\frac{\mathbf{28}}{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta }}$and$\mathit{y}\mathbf{=}\frac{\mathbf{28}}{\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\theta }}$

Step-by-step solution

Step 1. Given information

A triangle is given with a side of 28.

Step 2. Concept used

Only one side is given in the question. And for other sides, use trigonometric ratios as-

$\begin{array}{l}\Rightarrow \sin \theta =\frac{perpendicular}{hypotenuse}=\frac{P}{H}\\ \Rightarrow \cos \theta =\frac{base}{hypotenuse}=\frac{B}{H}\\ \Rightarrow \tan \theta =\frac{perpendicular}{base}=\frac{P}{B}\end{array}$

Step 3. Calculation

From given figure,

$\begin{array}{l}\Rightarrow \cos \theta =\frac{B}{H}\\ \Rightarrow \cos \theta =\frac{x}{28}\\ x=\frac{28}{\cos \theta }\end{array}$

$\begin{array}{l}\Rightarrow \sin \theta =\frac{P}{H}\\ \Rightarrow \sin \theta =\frac{y}{28}\\ y=\frac{28}{\sin \theta }\end{array}$