Answer :
To find the area of the triangle with given measurements C=133.6°, a=46.1 ft, and b=36.6 ft, use the formula Area = (1/2) * a * b * sin(C). Converting the angle to radians and calculating using a calculator gives the area as approximately 612.49 square feet.
To find the area of a triangle when two sides and the included angle are known, we use the formula:
Area = (1/2) * a * b * sin(C)
Given the values:
- a = 46.1 ft
- b = 36.6 ft
- C = 133.6°
First, convert the angle C from degrees to radians, as trigonometric functions typically use radians:
C (in radians) = 133.6° * (π/180)
C ≈ 2.331 radians
Now, plug the values into the formula:
Area = (1/2) * 46.1 * 36.6 * sin(2.331)
Using a calculator to find sin(2.331):
sin(2.331) ≈ 0.728
So the area is:
Area ≈ (1/2) * 46.1 * 36.6 * 0.728
Area ≈ 612.49 square feet
Thus, the area of the triangle is approximately 612.49 square feet.
The area of the triangle is approximately 531.9 square feet.
- Identify the given values and the formula for the area of a triangle using two sides and the included angle:
[tex]\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \][/tex]
Given: [tex]\( a = 46.1 \)[/tex] ft, [tex]\( b = 36.6 \)[/tex] ft, [tex]\( C = 133.6^\circ \).[/tex]
- Convert the angle to radians if needed:
[tex]\[ \text{Angle in radians} = 133.6^\circ \times \frac{\pi}{180} \approx 2.331 \, \text{radians} \][/tex]
- Calculate the area using the given values:
[tex]\[ \text{Area} = \frac{1}{2} \times 46.1 \times 36.6 \times \sin(133.6^\circ) \][/tex]
[tex]\[ \sin(133.6^\circ) \approx 0.6691 \][/tex]
[tex]\[ \text{Area} \approx \frac{1}{2} \times 46.1 \times 36.6 \times 0.6691 \approx 531.9 \, \text{square feet} \][/tex]