Question

On each right triangle ,find the tangent of each angle that is not the right angle.Number 2.

Answer 1

Given the triangle ABC, you know that:

`\begin{gathered} AB=10 \\ AC=6 \\ BC=8 \end{gathered}`

You can identify that the small square in the vertex C of the triangle is a Right Angle (an angle that measures 90 degrees). Therefore, you have to find the tangent of the other two angles:

`\begin{gathered} \angle A \\ \angle B \end{gathered}`

By definition:

`tan\theta=(opposite)/(adjacent)`

Then:

- For angle A, you can identify that:

`\begin{gathered} \theta=A \\ opposite=BC=8 \\ adjacent=AC=6 \end{gathered}`

Therefore:

`\begin{gathered} tan(A)=(8)/(6) \\ \\ tan(A)=(4)/(3) \end{gathered}`

- For angle B:

`\begin{gathered} \theta=B \\ opposite=AC=6 \\ adjacent=BC=8 \end{gathered}`

Therefore, you get:

`\begin{gathered} tan(B)=(6)/(8) \\ \\ tan(B)=(3)/(4) \end{gathered}`

Hence, the answer is:

`\begin{gathered} tan(A)=(4)/(3) \\ \\ tan(B)=(3)/(4) \end{gathered}`