Question

Precalculus:Consider the right triangle where a = 3mi and alpha = 45 degrees Find an approximate value (accurate up to three or more decimals) of each of the following. Give the angle in degrees.

Answer 1

Given:

$\begin{gathered} a=3mi \\ \alpha=45\degree \end{gathered}$

Required:

To find the value of beta, b and c.

Explanation:

The given triangle is right triangle.

Therefore,

$\begin{gathered} \sin\alpha=\frac{a}{c} \\ \\ \sin45=\frac{3}{c} \\ \\ 0.7071=\frac{3}{c} \\ \\ c=\frac{3}{0.7071} \\ \\ c=4.2426mi \end{gathered}$

Now

$\begin{gathered} \tan\alpha=\frac{a}{b} \\ \\ \tan45=\frac{3}{b} \\ \\ 1=\frac{3}{b} \\ \\ b=3 \end{gathered}$

The sum of the angle in triangle is 180 degree.

Therefore

$\begin{gathered} 90+45+\beta=180 \\ \beta=180-90-45 \\ \beta=45\degree \end{gathered}$

Final Answer:

$\begin{gathered} b=3mi \\ c=4.2426mi \\ \beta=45\degree \end{gathered}$