A man sets a 3ft high transit on level ground 12 ft away and perpendicular to a wall?

Question

He then points the transit at the top of the roof and notes the azimuth as 51.34 degrees.
How high is the wall?

He then rotates the transit and points it at the corner where the pitched roof and wall meet. He notes that the rotation was 36.86 degrees to the right. The new azimuth is 13.5 degrees.
What is the pitch of the roof?

Answer 1

yikes... I remember doing this in grade 10. I don't know if this makes sense, but for the height of the wall, I got 228.02 feet.

180 degrees - 51.34 - 90 (the angle of the wall) = 38.66 degrees (the missing angle)
then,
a / sin a = b / sin b
a / sin 90 = 12 / sin 38.66

cross multiply and divide, and you get 19.21 (the length of the hypotenuse).
Then a2 + b2 = c2, so the missing length is 225.02, but you have to add 3 feet, which is the height of the transit. So, you get 228.02 feet.

Phew! Hope that's right!