Question

brian is going to replace the tile on a triangular section of his floor. the section of the floor is shown.
what is the area, rounded to the nearest tenth, that brian needs to replace? enter the answer in the box.
square feet

Explanation:

Step1: Select area formula for SAS

We use the formula for the area of a triangle with two sides and included angle: $Area = \frac{1}{2}ab\sin(C)$, where $a$ and $b$ are sides, $C$ is the included angle.

Step2: Plug in known values

Use sides $a=5$ ft, $b=10$ ft, included angle $C=130^\circ$.
$Area = \frac{1}{2} \times 5 \times 10 \times \sin(130^\circ)$

Step3: Calculate the value

First compute $\sin(130^\circ) \approx 0.7660$, then:
$Area = \frac{1}{2} \times 50 \times 0.7660 = 25 \times 0.7660 = 19.15$

Step4: Round to nearest tenth

$19.15$ rounded to the nearest tenth is $19.2$.

Answer:

19.2 square feet