Determine the area of a triangle having the following measurements. Round your answer to two decimal places.
128Ab=°, =8, and c=15
A) 56.74 sq. units
B) 47.28 sq. units
C) 37.82 sq. units
D) 42.55 sq. units
E) 52.01 sq. units

Question

Quizplus · Accepted Answer

The area of a triangle can be calculated using the formula $ \frac{1}{2}ab\sin(C) $, where $a$ and $b$ are the lengths of two sides, and $C$ is the angle between them. Given $a = 8$, $c = 15$, and the angle $A = 128^\circ$, it seems there might be a slight confusion in the notation since $c$ typically represents the length of the side opposite angle $C$ in triangle notation, and the angle provided is labeled $A$. Assuming the intention is to calculate the area with sides $a = 8$ and another side (presumably $b$, though not explicitly given) with the angle between them as $128^\circ$, and assuming $c = 15$ is not directly used in the calculation due to the provided formula not accommodating three sides directly without an angle, we proceed with an assumption that might involve using sides $a$ and $b$ with the given angle. However, without a clear $b$ or a direct application of $c$, we'll correct the approach to focus on the information given.If the angle $A = 128^\circ$ is between sides $a = 8$ and $c = 15$, then the formula for the area becomes $ \frac{1}{2}ac\sin(A) $. Plugging in the values:$$ \text{Area} = \frac{1}{2} \times 8 \times 15 \times \sin(128^\circ) $$Using a calculator to find $\sin(128^\circ)$ and then calculating the area:$$ \text{Area} = 4 \times 15 \times 0.78801 \approx 47.28 $$Therefore, the area of the triangle is approximately 47.28 square units.

Determine the Area of a Triangle Having the Following Measurements