Question

Find the tangent of each angle that is not the right angle. Drag and drop the numbers into the boxes to show the tangent of each angle. B 76 tan ZA tan ZB 2.45 0.38 0.93

Answer 1

From the trignometric ratio of right angle triangle :

The ratio for the tangent of any angle of right angle triangle is the ratio of the side Opposite to that angle to the adjacent side of that angle :

`\tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}}`

In the given triangle :The side opposite to the angle A is BC and the adjacent side AC

So,

`\begin{gathered} \tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}} \\ \tan A=(BC)/(AC) \end{gathered}`

In the figure : we have AC = 76, BC = 31 and AB = 82.1

Substitute the value and simplify :

`\begin{gathered} \tan A=(BC)/(AC) \\ \tan A=(31)/(76) \\ \tan A=0.407 \\ \tan A=0.41 \end{gathered}`

Thus, tan A = 0.41

Now, the side opposite to the angle B is AC and the adjacent side is BC

thus :

`\begin{gathered} \tan \theta=\frac{Opposite\text{ Side}}{Adjacent\text{ Side}} \\ \tan B=(AC)/(BC) \end{gathered}`

In the figure : we have AC = 76, BC = 31 and AB = 82.1

Substitute the value and simplify :

`\begin{gathered} \tan B=(AC)/(BC) \\ \tan B=(76)/(31) \\ \tan B=2.451 \end{gathered}`

tan B = 2.451

Answer :

tanA = 0.41

tanB = 2.45