Answer:
see below
Step-by-step explanation:
The angle where chords cross is the average of the intercepted arcs. Here, that is ...
(37° +46°)/2 = (83°)/2 = 41.5°
Angle SUT is 41.5°.
_____
<em>Comment on the error</em>
The measure of an arc cannot be arbitrarily said to be the same as the angle where the chords cross. It will be the same if (a) the chords cross at the circle center, or (b) the opposite intercepted arc has the same measure. Neither of these conditions hold here.
Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
<em></em>
Therefore, the angle between their paths is <em>100.8°</em>
2)The circumference or perimeter of a circle with radius is
. Given
. Therefore,
Thus the radius is , diameter
and area