Answer:
69 degrees
Step-by-step explanation:
See attached image.
Answer:
The probability that a randomly placed point falls within the smaller, inner circle is 25/64
Step-by-step explanation:
The remaining part of question is attached
Solution
The area of smaller circle is

The area of large circle is

Area of the shaded region
Area of large circle - area of small circle

Probability that the point falls in the region of smaller circle is

Well the formula for the area of a trapezoid is as follows:
A=

where
a and
b are both base measures (a trapezoid has a top and bottom base)
.
Therefore, if all three have the same base length (the top and bottom lengths themselves being different yet the same on all three), the trapezoid with the greatest angle measure would have the greatest are. This is because with a greater angle measure comes a greater height (Pythagorean theorem).<span />
Answer:
Angle θ would be about 17.1 degrees.
Step-by-step explanation:
To figure out what Angle θ is, first we have to find the hypotenuse. You can easily do that by find the square root of BC² + AC².
c = √4² + 13²
Square 4 and 13 to get 16 and 169 respectively.
c = √16 + 169
Add 16 and 169 to get 185.
c = √185
Find the square root of 185 (I'll round to the nearest tenth.)
c = 13.60147 ≈ 13.6 units
To find angle β, divide AC by AB and find the inverse sine of that.
β = arcsin(13/13.6)
Divide 13 by 13.6. Round to the nearest thousandth.
β = arcsin(0.955)
β ≈ 1.2723 rad
To convert radians to degrees, multiply the radians by 57.2957795 for an approximate amount.
β ≈ (1.2723 * 57.2957795)°
β ≈ 72.8974203 ≈ 72.9 degrees
Now subtract 72.9 from 90 to get angle θ's measure of 17.1 degrees.