find the cosine and sine of 210 degrees round your answers to the nearest hundredth if necessary.

This can be answered by understanding the unit circle and the Pythagorean theorem. 210° can form a right triangle with the x-axis in quadrant III. To get the value of the angle formed between the circle’s radius and the x-axis, divide the angles of the 2 quadrants from 210°.
210°-90-°90° = 30°
In the Pythagorean theorem has a ratio of 1,2, √3 of the sides of the triangle. In a unit circle, the opposite side from the 30° angle is 1. The adjacent side is √3 while the hypotenuse is 2. With this info, we can use SOHCAHTOA.
So,
Sin(∅) = opposite / hypotenuse
Sin(30°) = ½ =0.5
Cos(∅) = adjacent/hypotenuse
Cos(30°) = sqrt.3/2 = 0.86602 = 0.87

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

8.4 10.4 8.9 10.9 have a good day