Chapter 8.6, Problem 8CE

To determine

To state two equation which can be used to find side of the triangle.

Explanation of Solution

Given:

The angles of triangle are ${41}^{\circ },{49}^{\circ },{90}^{\circ }.$

In the given figure value of one side of the triangle is 100.

Method:

By using basic formula of trigonometry.

Calculation:

  

In given triangle

  $\begin{array}{l}\sin {41}^{\circ }=\frac{x}{100}\\ \Rightarrow x=\sin {41}^{\circ }\times 100\mathrm{...}(1)\end{array}$

  $\begin{array}{l}\cos {49}^{\circ }=\frac{x}{100}\\ \Rightarrow x=\cos {49}^{\circ }\times 100\mathrm{...}(2)\end{array}$

Equation (1) and (2) can be used to find the value of x.