Answer:
16π/9
Step-by-step explanation:
40°/360° = 1/9
40° is 1/9 of a circle
Arc length = 1/9 of circumference = (1/9)2πr = 16π/9
We can solve this by first finding the diameter of the two semicircles. We know that the width of the rectangle is 27 inches, which also happens to be the diameter of the circle.
The circumference of a circle is 2πr or πd. The problem says that it is a semicircle, however, it says that there are two of them. Since the two semicircles are the same size, we know that they can combine to form one circle, so we can just find the circumference of one circle to account for both of the semicircles:
C=27π inches
We also know that the length of the rectangle is 60 inches. We only want to find the perimeter of the frame, so we don't have to account for the widths of the rectangle because it is inside the frame. Therefore, the two sides of the rectangle together are 120 inches. Now we can add this to the circumference we found:
120+27π inches or 204.78 inches (depends on what your teacher is asking for)
Answer:
8
Step-by-step explanation:
*whispers* (there is a calculator online for that.)
Also the formula is a² + b² = c².
8 feet to 3 yards is in the simplest form
Answer:
1045.01 rounded to the nearest hundredth
Step-by-step explanation:
First, we can draw this out. The angle of depression is the angle formed by the object at the top and the line formed by the object at the top and the object at the bottom.
If the truck on the left is truck A and the truck on the right is truck B, with the helicopter being the circle on top, there is one 60 degree angle of depression and one 20 degree one. If we make a point at the point in the road the helicopter is straight above, and we connect the points, we can form two right triangles, as shown. If we can calculate the lengths of sides x and y, we can add them up to find the length between the two trucks.
Starting with side x, we know one angle and the side length adjacent to that angle. We want to find the length opposite that angle. One formula that encompasses this is tan(θ) = opposite/adjacent. Therefore, tan(60) = x/500
tan(60) = x/500
multiply both sides by 500 to isolate the x
tan(60) * 500 = x
x = 866.0254
Similarly, with side y, we can say that tan(20) = y/500 and
tan(20) * 500 = y
y= 181.9851
The distance between the two trucks can be shown as x+y, so x+y= 1045.01 rounded to the nearest hundredth