# Thread: Angle in a tetrahedron

1. ## Angle in a tetrahedron

The diagram (sorry, had a bug with photoshop) shows a tetrahedron
AD is perpendicular to both AB and AC

AB=10cm
AC=8cm
Angle BAC = 90 degrees

Find the size of angle BDC

Please could someone help me out through this step by step? I know what to do to get the answer just not how to do it.

2. Originally Posted by Mukilab
The diagram (sorry, had a bug with photoshop) shows a tetrahedron
AD is perpendicular to both AB and AC

AB=10cm
AC=8cm
Angle BAC = 90 degrees

Find the size of angle BDC

Please could someone help me out through this step by step? I know what to do to get the answer just not how to do it.
1. Use the 3 right triangles to calculate the lengths of the triangle BDC.
Spoiler:
$\displaystyle \sqrt{89}$, $\displaystyle \sqrt{125}$, $\displaystyle \sqrt{164}$

2. Use the Cosine rule to calculate the angle $\displaystyle \angle(BDC)$
Spoiler:
I've got $\displaystyle \angle(BDC) \approx 76.29^\circ$

3. I had the three lengths, just didn't know the cosine law. Thanks