# In Trigonometry if you have the measurements of a right angled triangle ABC and you know that the right angle is at B and BC = 4cm and C = 40 degrees and you are told to find AB. HOW ON EARTH DO...

In Trigonometry if you have the measurements of a right angled triangle ABC and you know that the right angle is at B and BC = 4cm and C = 40 degrees and you are told to find AB. HOW ON EARTH DO YOU FIND IT?????????????????????

Please help!

Thought I understood but this is one MAJOR curveball!

All help greatly appreciated!

Thank you!

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### 1 Answer

First, draw the figure described in the problem. See image below for reference.

In the triangle ABC, notice that BC is the side adjacent to angle C. While AB is the side opposite to angle C. And since it is a right triangle, tangent function can be used to solve for AB.

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

Using angle C as theta, then opposite=AB and adjacent=BC.

`tan C=(AB)/(BC)`

`tan 40^o=(AB)/4`

To isolate AB, multiply both sides by 4.

`4*tan40^o=(AB)/4*4`

`4*tan40^o=AB`

`3.36=AB`

**Hence, the length of side AB is 3.36 cm.**

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Thank you thank you thank you!

Helped alot!