I have two questions...

#1
if the radius of the two areas is 12in find the length of a chord of an arc of 45, 35, and 60 degrees.

#2 the bases of a trapezoid are 30in and 9in and the nonparallel sides are 10in and 17in. Find the area.

Sure! Let's break down each question and find the answers step by step.

#1 - Finding the length of a chord of an arc:
To find the length of a chord of an arc, we need to know the radius of the circle and the measure of the arc. In this case, the radius is given as 12 inches.

To find the length of a chord, we need to apply some trigonometry. The formula we can use is:
Chord length = 2 * Radius * sin(Angle/2)

Now, let's calculate the length of the chord for each given angle:
For an arc of 45 degrees:
Chord length = 2 * 12 * sin(45/2)

For an arc of 35 degrees:
Chord length = 2 *12 * sin(35/2)

For an arc of 60 degrees:
Chord length = 2 * 12 * sin(60/2)

By substituting the values and evaluating the trigonometric functions, you can find the length of each chord.

#2 - Finding the area of a trapezoid:
The area of a trapezoid can be found by using the formula:
Area = (base1 + base2) * height / 2

In this case, the given bases are 30 inches and 9 inches, and the height is 10 inches. However, it's important to note that a trapezoid has nonparallel sides of length 10 inches and 17 inches.

Since the nonparallel sides are not given as the bases, we need to first find the lengths of the bases using the given side lengths. We can do this by using the Pythagorean theorem. Let's denote the nonparallel sides as 'a' and 'b'.

Using the Pythagorean theorem, we have:
a^2 = (30 - 9)^2 + 10^2
b^2 = 17^2 - 10^2

Once you find 'a' and 'b', substitute them into the area formula:
Area = (30 + 9) * height / 2

By calculating the values and substituting them into the formula, you can find the area of the trapezoid.