The lengths of two sides of a triangle are 6cm and 4cm and the angle between them is 130degree. What is its area?
Area is 1/2 base * height.
Let the side of length 6 be the base.
Extend it so you can drop an altitude from the end of side with length 4.
Now you have a right triangle with hypotenuse=4, base angle = 50 deg (180-130).
So, the height is given by
h/4 = sin(50)
h = 3.06
So, the area is just 1/2 * 3.06 * 6 = 9 approx.
Well, it seems like we have a triangle with some interesting lengths and angles. In order to find the area, we can use the formula: Area = (1/2) * a * b * sin(C). In this case, we have side a as 6cm, side b as 4cm, and angle C as 130 degrees.
Now, let me grab my trusty calculator... *beep boop beep*
After doing some calculations, it looks like the area of this triangle is... a complete mystery! Why? Because the angle given, 130 degrees, is larger than 180 degrees. This means that the triangle simply doesn't exist in normal Euclidean geometry. It's a bit like trying to find Bigfoot riding a unicorn!
But don't worry, this little triangle puzzle serves as a reminder that not everything is possible, even in the world of mathematics. So, let's keep hunting for those unicorns and leave this triangle in the land of make-believe! 🦄
To find the area of a triangle, we can use the formula:
Area = (1/2) * base * height
In this case, the two given sides of the triangle are 6cm and 4cm. The angle between them is 130 degrees.
To find the height of the triangle, we need to use trigonometry. Let's assume that the side of length 6cm is the base of the triangle. We can use the sine function to find the height. The sine of an angle is equal to the opposite side divided by the hypotenuse.
sin(130 degrees) = height / 4cm
To find the height, we can rearrange the equation:
height = sin(130 degrees) * 4cm
Using a calculator, we can find that sin(130 degrees) is approximately 0.766.
height = 0.766 * 4cm = 3.064cm
Now that we have the base length (6cm) and the height (3.064cm), we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Area = (1/2) * 6cm * 3.064cm
Area ≈ 9.192cm²
Therefore, the approximate area of the triangle is 9.192 square centimeters.
To find the area of a triangle, we need to know the lengths of two sides and the angle between them. In this case, we have the lengths of two sides as 6 cm and 4 cm, and the angle between them is 130 degrees.
To find the area of the triangle, we can use the formula:
Area = (1/2) * a * b * sin(C)
Where:
a and b are the lengths of the two sides of the triangle,
C is the angle between them.
In this case, a = 6 cm, b = 4 cm, and C = 130 degrees. However, the formula requires the angle to be in radians, so we need to convert the angle from degrees to radians.
To convert degrees to radians, we use the following formula:
radians = degrees * (Ï€ / 180)
So, let's calculate the value of the angle in radians:
130 degrees * (Ï€ / 180) = 2.268 radians (approximately)
Now, we can substitute the values into the area formula:
Area = (1/2) * 6 cm * 4 cm * sin(2.268 radians)
To find the sine of an angle (2.268 radians), we can use a scientific calculator or refer to a trigonometric table.
Using a scientific calculator or trigonometric table, if we find that sin(2.268 radians) = 0.824,
we can now calculate the area:
Area = (1/2) * 6 cm * 4 cm * 0.824
= 4.968 cm² (approximately)
Therefore, the area of the triangle is approximately 4.968 square centimeters.