Question

Solve for the unknown sides of the triangle below. If a value is not an integer round it to the nearest hundredth.right triangle, acute angle 10 degrees opposite side a, hypotenuse is 12, side b is opposite angle Bside a=Answerside b=Answerangle B=Answer degrees

Answer 1

`\begin{gathered} a=2.08 \\ b=11.82 \\ m\lt B=80 \end{gathered}`

Explanation:

To solve the missing sides using trigonometric ratios, which are described by the following equations:

`\begin{gathered} sin\left(angle\right)=(opposite)/(hypotenuse) \\ cos\left(angle\right)=(adjacent)/(hypotenuse) \\ tan\left(angle\right)=\frac{opposite\text{ }}{adjacent} \end{gathered}`

Then, for the missing sides, use the sin and cos relationship:

`\begin{gathered} sin\left(10\right)=(a)/(12) \\ a=12*sin\left(10\right) \\ a=2.08 \\ \\ cos\left(10\right)=(b)/(12) \\ b=12*cos\left(10\right) \\ b=11.817 \\ \text{ Rounding to the nearest hundredth:} \\ b=11.82 \end{gathered}`

Since all intern angles of a triangle must add up to 180 degrees, solve for angle ''B'':

[tex]\begin{gathered} m