Answer:
θ = 38°
Step-by-step explanation:
The lower right triangle is congruent to the upper left triangle, so we have θ and 20° being the two acute angles in the triangle. The law of sines tells you ...
sin(θ)/9 = sin(20°)/5
sin(θ) = (9/5)sin(20°)
θ = arcsin(9/5·sin(20°)) ≈ 38°
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Another solution to the triangle is θ = 180° -38° = 142°. The diagram clearly shows θ as an acute angle, so we take this second solution to be extraneous.
B
The purple balls constitute 1/3 of the amount of balls there, so you’re that likely to pluck one out.
<h3>
Answer:</h3>
The transformation is a rotation.
<h3>
Step-by-step explanation:</h3>
The incorrect answers can be ruled out as follows:
- dilation would change the size, but not the directions of the lines
- reflection would change the DEF ordering from clockwise to counterclockwise
- translation would move the figure, but not change the directions of the lines
The image is the same size as the original. Each of the sides of the triangle is moved through the same angle. The transformation is a rotataion.
The center of rotation can be found as the point of intersection of the perpendicular bisectors of DD', EE' and FF'
