what is the area of the triangle to the nearest tenth 13m 8m 28 degrees
Using the formula for the area of a triangle:
area = (1/2) * base * height
We can first find the height of the triangle by using trigonometry:
sin(28°) = height/13
height = 13 * sin(28°)
height ≈ 6.02
Now we can plug in the values for the base and height:
area = (1/2) * 8 * 6.02
area ≈ 24.1
Therefore, the area of the triangle is approximately 24.1 square meters to the nearest tenth.
To find the area of a triangle with two sides and the included angle given, you can use the formula:
Area = (1/2) * side1 * side2 * sin(angle)
Given the information you provided:
Side1 = 13m
Side2 = 8m
Angle = 28 degrees
Let's substitute these values into the formula:
Area = (1/2) * 13m * 8m * sin(28 degrees)
First, let's convert the angle from degrees to radians because the sine function in the formula uses radians.
Angle in radians = (28 degrees * π) / 180
Angle in radians ≈ 0.48869 radians
Substituting these values and evaluating the expression:
Area ≈ (1/2) * 13m * 8m * sin(0.48869 radians)
Area ≈ (1/2) * 13m * 8m * 0.4695
Area ≈ 31.4368 square meters
Therefore, the area of the triangle is approximately 31.4 square meters to the nearest tenth.