Question

what is the area of the triangle? round your answer to the nearest tenth.
triangle with vertices a, b, c. side ab is 13, side ac is 14, angle at a is 65°.

Explanation:

Step1: Recall area formula for SAS triangle

The formula for the area of a triangle with two sides $a, b$ and included angle $\theta$ is $\text{Area} = \frac{1}{2}ab\sin\theta$.

Step2: Substitute given values

Here, $a=14$, $b=13$, $\theta=65^\circ$.
$\text{Area} = \frac{1}{2} \times 14 \times 13 \times \sin(65^\circ)$

Step3: Calculate intermediate values

First compute $\frac{1}{2} \times 14 \times 13 = 91$. $\sin(65^\circ) \approx 0.9063$.

Step4: Compute final area

$\text{Area} \approx 91 \times 0.9063 \approx 82.5$

Answer:

82.5