Chapter 6.1, Problem 54E

To determine

To explain:

Short Paragraph explaining law of sines used for solving triangle.

Answer to Problem 54E

Short Paragraph explaining law of sines used for solving triangle is explained as below.

Explanation of Solution

Given information:

  $b=50°,C=90°,a=10$

Consider,

  $b=50°,C=90°,a=10$

Sum of the angles of triangle is $180°$

So,

  $\begin{array}{l}A+B+C=180°\\ A+50°+90°=180°\\ A+140°=180°\\ A=40°\end{array}$

To find out other two side lengths, law of sines used,

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

By substituting above values in equation will provide value for all side lengths.

This can be solved by easy method.

This being a right angle triangle the trigonometric formulas will be useful and are easier for solving.

The side length can also be get by using Pythagoras theorem.