Answer:
Step-by-step explanation:
You have to know definitions for sin and cos. This visual definition might work for you.
cos is horizontal. sin is vertical.
For a right triangle with one other angle θ specified, let A be the vertex with angle θ.
Put A at the origin. Let B be the vertex with the right angle. Put B on the x axis. Let C be the other vertex.
Angle BAC is θ.
Angle ABC is the right angle.
Angle BCA is 90° - θ.
Side AB is on the x axis, length b.
Side AC is the hypotenuse, length h.
Side BC is parallel to the y axis, length c.
Draw a circle centered origin radius one.
If necessary, extend the hypotenuse AC to cross the unit circle at point Y.
Draw a segment perpendicular to the x axis from point Y to point X on the x axis, parallel to side CB.
Angle XAY is θ.
Side AY is radial with length one.
Side AX is horizontal with length cos(θ).
Side XY is vertical with length sin(θ).
Radial side AC has length h.
Horizontal side AB has length b = h cos(θ).
Vertical side BC has length c = h sin(θ).
1) h = 22, θ = 21°, x on diagram is vertical BC,
x = 22 sin(21°)
2) h = 15m, θ = 33°, x on diagram is horizontal AB,
x = 15m cos(33°)
3) h = 10, θ = 32°. Ignore diagram labels A B C,
x on diagram is horizontal AB.
x = 10 cos(32°)
y on diagram is vertical BC.
y = 10 sin(32°)
4) h = length of ramp, θ = 30°, h sin(30°) = 4 feet.
4a) radial h = 4 feet / sin(30°)
4b) horizontal distance ramp to wall = h cos(30°)
= ( 4 feet / sin(30°) ) cos(30°)
