Answer:
B. 57
Step-by-step explanation:
You can solve the triangle using the Law of Cosines, then find the required angle using the Law of Sines. Or, you can estimate it based on the fact that the angle shown is very nearly 90°.
If ∠B were 90°, then the value of ∠C would be ...
∠C ≈ arctan(21/14) ≈ arctan(1.5) ≈ 56.3°
Since ∠B is slightly smaller, ∠C will be slightly larger. The nearest value slightly larger than 56.3° is choice B, 57°.
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Doing this the long way, you get ...
b² = a² + c² - 2ac·cos(B) = 14² +21² -2(14)(21)cos(89°) ≈ 626.738
b ≈ √626.738 ≈ 25.035
Then angle C is given by the law of sines as ...
sin(C)/c = sin(B)/b
C = arcsin(c/b·sin(B)) ≈ arcsin(0.838707) ≈ 57.004°
m∠C ≈ 57°
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Many graphing calculators can solve triangles, as can phone or tablet apps.
<span>We need to divide 72 rolls into 2 groups so that their ratio is 3:5. First, we can see that the ratio of 3:5 tells us there is 8 separate groups of rolls. Now its easy, since we have 72 rolls and we need to divide them into 8 equal groups: 72/8=9. So each group has 9 rolls. Now we separate them into groups with the ratio 3:5, so: 3*9:5*9 and that is: 27 rolls and 45 rolls. </span>
Answer:
The answer is C
Step-by-step explanation:
After a translation, the measures of the sides and angles on any triangle would be the same since translation only involves changing the coordinates of the vertices of the triangle.
After a rotation, the measures of the sides and angles of a triangle would also be the same. Similar to translation, the proportion of the triangle is unchanged after a rotation.
After a reflection, the triangle's sides and angles would still be the same since reflection is a rigid transformation and that proportion of the sides and angles are not changed.
