I have the question "Calculate the angle between the face BCE and the base ABCD in the pyramid pictured below, giving your answer to 1 decimal place."
I assume the angle we are trying to find is B and so I draw a triangle DBE and use the cosine rule to get the answer of 74.6 degrees. However the answer should be 79 degrees.
Here is my working:
Is the angle B the correct angle which I need to find or is it a different angle ? Because I know the method to use but the angle B is giving an incorrect value so it can't be this.
Best Answer
Let the midpoint of $AC$ be $M$ and the midpoint of $AD$ be $N$. Then $AC$ is perpendicular to $EM$. We can find the length of $NE$ using Pythagoras:
$NE = \sqrt{8^{2} - 1.5^{2}} = \frac{\sqrt{247}}{2}$
Now we need to find $\angle ENM$
Again, since $ENM$ forms a right angled triangle, $\angle ENM = arccos(\frac{1.5}{\frac{\sqrt{247}}{2}}) = 78.9955... \approx 79$degrees
I can include a diagram if this is hard to follow.
Edit: diagram included: