Maths help !?!? PLEASE! Trigonometry

I need a little help for my maths homework.. I already did them but Im not sure if they are right, sooo.. please help? Make sure your answers are correct though, don't really wanna confuse myself! Thanks to anyone who takes the time to answer this! :) :) :)


1. A ladder 12m long standing on level ground has it's foot 4 metres from a vertical wall against which it leans. Find the angle between the ladder and the horizontal.

2. When the altitude of the sun is 55 degrees (measured from the ground), a tree casts a shadow 15 m long. Find the height of the tree.

3. The gradient of a road is quoted as 1 in 10. This means that the rise of 1 unit for every 10 units moved horizontally. What angle does this road make with the horizontal?

4. The longest side of a rectangle makes an angle of 37 degrees with the diagonal which is 12 cm in length. Calculate the width of the rectangle.

5. A marksman 200 metres from the target and level with it, aims 3 metres above the bull eye and hits it. At what angle was his rifle inclined to the horizontal?

6. A 5 metre ramp slopes at 19 degrees to the horizontal. Calculate the difference in height between the 2 ends.




PLEASE HELP! ):

Tan = opposite/adjacent
Sin = opposite/hypotenuse
Cos = adjacent/hypotenuse

1) cos = adjacent/hypotenuse
| \
| \
| \ hypotenuse
| \ 12 m
| \
|_ _ _\ <-- let unknown angle be 'y'
adjacent
4 m

cos y = 4/12
To find angle size of y, use a calculator.
Press the buttons: shift, cos, 4 ÷ 12, then enter.
You should come up with 70.52877937. Round it.

Therefore, the angle between the ladder and horizontal is 70.5°, rounded to 1 decimal place.

2) tan = opposite/adjacent
Let the height of the tree be 'y'
tan 55 = y/15
times 15 both sides
1.428148007 = y

Therefore, the height of the tree is 1.4 m (to 1 decimal place).