Question

Solve for the length of BA and BC, round your answer to 1 decimal place

Answer 1

`BA = 6.0`

`BC = 13.4`

Explanation:

Given

The attached triangle

Solving (a) BA

Considering the tangent of angle C, we have:

`tan\ C = (BA)/(AC)\\`

This gives:

`tan\ 25 = (BA)/(12)`

Make BA the subject

`BA = 12 * tan\ 25`

`BA = 12 * 0.4663`

`BA = 6.0` --- approximated

Solving (a) BC

Using Pythagoras theorem

`BC^2 = BA^2 + AC^2`

`BC^2 = 6.0^2 + 12^2`

`BC^2 = 180`

Square root of both sides

`BC = \sqrt{180`

`BC = 13.4`