3) tan = opposite/adjacent
|\
| \
| \
1 | \ road
| \
|___\ <-------- let unknown angle be 'z'
10
tan z = 1/10
Shift + tan + 1/10 = z
= 5.71° (to 2 decimal places)
Therefore, the road makes a 5.71° angle with the horizontal (to 2 decimal places).
4) sin = opposite/hypotenuse
Let the width be 'w'
sin 37 = w/12
times each side by 12
0.6018150232 x 12 = w/12 x 12
7.221780278 = w
Therefore, the width of the rectangle is 7.2 cm (to 1 decimal place).
5) I don't really understand this question, but I'm guessing this is how it works:
Let the angle between the rifle and horizontal be 'y'.
tan y = 3/200
shift + tan + 3/200 = 0.85937...
= y
Doesn't sound right... I'm not sure. Sorry! However, I'm pretty sure the other answers are right.
6) sin = opposite/hypotenuse
|\
| \
| \ 5 m
|_ _ \ <--- 19°
Let the height between the 2 ends be 'y'.
sin 19 = y/5
x 5 both sides
y = 1.62784...°
Therefore, the difference in height between the end of the ramp and horizontal is 1.6° (to 1 decimal place).
Hope I've helped! :)
EDIT: Sorry for the wonky diagrams - they were supposed to help, but turned out weird... :/
I kept some of the more legible ones, and I hope you can read it. :)