please check my answers.

1.Find the area of the sector of a circle.
r=11.8cm, theta-pi/7 radians
I got 31.2cmsquared
2.Find the radius of a circle in which a central angle of pi/6radian determines a sector of area 76square meters.
I got 17.03m
3.Find the measure(in radians) of a central angle of a sector of area 45 square inches in a circle of radius 8 inches.
I need help getting the answer
4.In this question you're suppose to approximate the length by finding the necessary arc length.

A tree 520m away subtends an angle of 4degrees. find the height of the tree.
I also need help on this one
THANKS ALOT

1. 31.24 yes

2.17.04 yes
3. total area = pi r^2 = pi(64)
angle/2pi =45/64 pi
angle = 45/32 = 1.41 radians = 80.6 degrees
4. r = 520
circumference = 2 pi (520) = 3267
4/360 = height/3267
height = 36.3

Thanks so much; This was of great help!

=D

Let's go through each question one by one:

1. To find the area of a sector of a circle, you can use the formula:
Area = (θ/2) * r^2
where θ is the central angle in radians and r is the radius of the circle.
In this case, the radius is given as 11.8 cm and the central angle is π/7 radians.
Plugging these values into the formula, we get:
Area = (π/7)/2 * (11.8)^2 ≈ 31.2 cm².

Your answer of 31.2 cm² is correct.

2. To find the radius of a circle given the area of a sector, you can rearrange the formula as follows:
r = sqrt(Area / (θ/2))
The area of the sector is given as 76 square meters and the central angle is π/6 radians.
Plugging these values into the formula, we have:
r = sqrt(76 / (π/6)) ≈ 17.03 meters.

Your answer of 17.03 meters is correct.

3. In order to find the measure in radians of a central angle of a sector, given its area and the radius of the circle, we can rearrange the formula for the area of a sector:
Area = (θ/2) * r^2
Since we now have the area and the radius, we need to solve for the central angle θ.
The area is given as 45 square inches and the radius is given as 8 inches.
Rearranging the formula, we get:
θ = (2 * Area) / r^2 = (2 * 45) / 8^2 = 0.5625 radians.

Therefore, the measure of the central angle is 0.5625 radians.

4. To approximate the height of a tree, given the distance to the tree and the angle it subtends, we can use trigonometry.
The angle is given as 4 degrees and the distance to the tree is 520 meters.
We can set up a right triangle, where the distance to the tree is the hypotenuse, and the height of the tree is the opposite side (relative to the angle).
Using trigonometric functions, we can find the height by using the formula:
height = distance * tan(angle)

height = 520 * tan(4 degrees).
To find the value of tan(4 degrees), you can use a calculator or a trigonometric table.
Evaluating this expression, we get approximately 36.19 meters as the height of the tree.