Question

Precal : Note: Triangle may not be drawn to scale. Suppose a = 3 and A = 15 degrees

Answer 1

Given:

In a right triangle at B,

`\begin{gathered} a=3 \\ A=15^(\circ) \end{gathered}`

To find:

The length of the sides b and c and angle B.

Step-by-step explanation:

Using the trigonometric ratio,

`\begin{gathered} sinA=(a)/(c) \\ \sin15^(\circ)=(3)/(c) \\ c=(3)/(\sin15^(\circ)) \\ c=11.59 \\ c\approx11.6 \end{gathered}`

Using the trigonometric ratio,

`\begin{gathered} \tan A=(a)/(b) \\ \tan15^(\circ)=(3)/(b) \\ b=(3)/(\tan15^(\circ)) \\ b=11.19 \\ b\approx11.2 \end{gathered}`

Using the angle sum property,

The angle B becomes,

`\begin{gathered} 90+15+B=180 \\ B=180-90-15 \\ B=75^(\circ) \end{gathered}`

Final answer:

The values are,

`\begin{gathered} b=11.2 \\ c=11.6 \\ B=75^(\circ) \end{gathered}`