Find the area of a triangle with sides of length 5 and 8 and included angle 74°. (Round your answer to one decimal place.)
A=1/2absin
A=1/2(8)(5)sin(74)
20sin(74)
=19.2
Well, let's solve this one step at a time! To find the area of a triangle, we can use the formula A = (1/2) * b * c * sin(A), where A represents the included angle and b and c represent the lengths of the sides.
So, plugging in the values we have, we get A = (1/2) * 5 * 8 * sin(74°).
Now, I must say, mathematicians love their trigonometry, but they tend to forget the importance of entertainment. So, let's use some clown math here!
If sin(74°) wanted to tell a joke, it would probably say, "Why did the angle go to the party? Because it knew how to sine and dance!"
Getting back to the calculation, after sin(74°) has finished its dance routine, we have:
A = (1/2) * 5 * 8 * 0.9613.
Now, it's time for some fancy math moves! Multiplying, dividing, and rounding, we find that the area of this triangle is approximately 19.2 square units.
So, the triangle's area is about 19.2 (but don't worry, this answer won't make you laugh as much as sin(74°)'s dance moves).
To find the area of a triangle with sides of length 5 and 8 and included angle 74°, we can use the formula:
Area = (1/2) * a * b * sin(C)
Where 'a' and 'b' are the lengths of the two sides, and 'C' is the included angle between those two sides.
Step 1: Convert the angle from degrees to radians.
Angle in radians = (Angle in degrees * π) / 180
Applying this formula to our angle of 74°:
Angle in radians = (74 * π) / 180 ≈ 1.29154
Step 2: Plug the values into the formula and calculate:
Area = (1/2) * 5 * 8 * sin(1.29154)
Evaluating the expression:
Area ≈ (1/2) * 5 * 8 * 0.96017 ≈ 19.20346
Step 3: Round the answer to one decimal place:
Area ≈ 19.2
Therefore, the area of the triangle is approximately 19.2 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 * b * sin(C)
Where "a" and "b" are the lengths of the two sides, and "C" is the included angle.
In this case, we have "a" = 5, "b" = 8, and "C" = 74°.
Plugging these values into the formula, we get:
Area = (1/2) * 5 * 8 * sin(74°)
Now, let's calculate the sin(74°) using a scientific calculator or an online calculator. The sin(74°) is approximately 0.9613.
Substituting this value into the formula, we have:
Area = (1/2) * 5 * 8 * 0.9613
Evaluating the expression, we find:
Area ≈ 19.226 square units
Therefore, the area of the triangle is approximately 19.2 square units (rounded to one decimal place).