find the area of the triangle B=72degree 30', a= 105, c=64
Area = 0.5ac*sinB,
Area = 0.5*105*64*sin72.5 = 3205.
To find the area of a triangle, you can use the formula:
Area = 0.5 * b * c * sin(B)
Given that B = 72° 30', a = 105, and c = 64, we can find the area using the formula.
Note: To calculate trigonometric functions in degrees, they need to be converted to radians first.
1. Convert degrees and minutes to decimal degrees.
B = 72° 30' = 72 + 30/60 = 72.5 degrees
2. Convert B to radians.
B (in radians) = B (in degrees) * (π/180)
= 72.5 * (π/180)
= 1.2661037 radians (rounded to 7 decimal places)
3. Calculate the area.
Area = 0.5 * a * c * sin(B)
= 0.5 * 105 * 64 * sin(1.2661037)
Calculating sin(1.2661037) gives us a decimal value.
4. Multiply the remaining values to find the area.
Area ≈ 0.5 * 105 * 64 * 0.93719
≈ 3153.2556
Therefore, the area of the triangle is approximately 3153.2556 square units.
To find the area of a triangle given two sides and the included angle, you can use the formula:
Area = (1/2) * a * c * sin(B)
Here, B represents the angle between sides a and c, a represents the length of side a, and c represents the length of side c.
To calculate the area of the triangle with the given values (B=72°30', a=105, c=64), we need to convert the angle B to radians since the sine function typically accepts angles in radians.
First, convert the angle B from degrees minutes seconds (DMS) to decimal degrees (DD):
72°30' = 72 + 30/60 = 72.5 degrees
Next, convert the angle B from degrees to radians:
B_radians = B * (π/180)
B_radians = 72.5 * (π/180) ≈ 1.2661 radians
Now that we have the angle B in radians, we can compute the area using the formula:
Area = (1/2) * a * c * sin(B_radians)
Area = (1/2) * 105 * 64 * sin(1.2661)
Using a calculator, evaluate sin(1.2661), and then substitute the value back into the formula to find the area.