The angle \theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant \text{IV}IVstart text, I, V, end text, and \sin(\theta_1)=-\dfrac{24}{25}sin(θ 1 )=− 25 24 sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 24, divided by, 25, end fraction . What is the value of \cos(\theta_1)cos(θ 1 )cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?

i found the answer
its 7/25

To find the area of the arena, you will need to find the areas of the rectangular spaces and the 2 semicircles. Because the formulas are given, I will just substitute in the values and show the work for finding the areas.

To find the perimeter, you will look at the distances of lines that take you around the space. Because two of these spaces are half circles, you will need to find the circumference of the full circle.

Also, the answers need to be given in meters, so all units given in centimeters will be divided by 100 to convert them to meters.

Perimeter:

C= 3.14 x 20 m

C = 62.8 meters

62.8 + 8 + 25 + 8 + 5 + 8 + 10 + 8 + 40= 174.8 meters for the Perimeter

Area:

A = 25 x 8

A = 200 square meters

A = 10 x 8

A = 80 square meters

A = 20 x 40

A = 800 square meters

A = 3.14 x 10^2

A = 314 square meters

Total Area: 314 + 800 + 80 + 200= 1394 square meters