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.

Step-by-step explanation:

The given triangle is right triangle.

Therefore,

`\begin{gathered} \sin\alpha=(a)/(c) \\ \\ \sin45=(3)/(c) \\ \\ 0.7071=(3)/(c) \\ \\ c=(3)/(0.7071) \\ \\ c=4.2426mi \end{gathered}`

Now

`\begin{gathered} \tan\alpha=(a)/(b) \\ \\ \tan45=(3)/(b) \\ \\ 1=(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}`