Find the areaof the triangle having the indicated sides and angle.
B = 72 degrees 30'
a = 105
c = 64
area = (1/2)(105)(64)sin 72.5º
= ....
Thank You
To find the area of the triangle, we can use the formula:
Area = (1/2) * a * c * sin(B)
Here, "a" and "c" represent the lengths of the given sides, and "B" represents the indicated angle. Let's calculate it step by step:
1. Convert the angle from degrees and minutes to decimal degrees:
B = 72 degrees + (30/60) degrees = 72.5 degrees
2. Convert the angle from degrees to radians:
B_radians = B * π / 180
= 72.5 * π / 180
3. Calculate the area using the formula:
Area = (1/2) * a * c * sin(B_radians)
= (1/2) * 105 * 64 * sin(72.5 * π / 180)
Now, we can use a calculator to find the numerical value of the sine function and calculate the area.