Find the area of the triangle.
b=125
c=162
<B=40
(b and c are the sides)
(<B is the angle)
Use the law of sines to solve for <C.
(sin <C)/c = (sin <B)/b
Use <A + <B + <C = 180 to solve for <A
Uze the law of sines to solve for a.
The triangle area is (1/2) c sin B * a
I worked it out. Can you tell me if these are right.
<C=56.4 degrees
<A=83.6 degrees
Area=10095.2
We have to round to the nearest tenths.
To find the area of a triangle, you can use the formula:
Area = (1/2) * b * c * sin(<B)
Given that b = 125, c = 162, and <B = 40:
Area = (1/2) * 125 * 162 * sin(40)
Now, let's evaluate this expression step by step:
Step 1: Calculate the sine of the angle. Since trigonometric functions generally work in radians, we need to convert the angle from degrees to radians.
sin(40°) ≈ sin(0.6981 radians) ≈ 0.6428
Step 2: Plug in the known values into the formula:
Area = (1/2) * 125 * 162 * 0.6428
Step 3: Simplify the expression:
Area ≈ 51,631.25
Therefore, the area of the triangle is approximately 51,631.25 square units.