Question

what is the area of the triangle? round your answer to the nearest tenth.
triangle with vertices a, b, c; side ac = 17, side ab = 19, angle at a is 51°

Explanation:

Step1: Recall SAS area formula

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, $a=17$, $b=19$, $\theta=51^\circ$. Substitute into the formula:
$$\text{Area} = \frac{1}{2} \times 17 \times 19 \times \sin(51^\circ)$$

Step3: Calculate intermediate values

First compute $17 \times 19 = 323$, then $\frac{1}{2} \times 323 = 161.5$. $\sin(51^\circ) \approx 0.7771$.
$$\text{Area} \approx 161.5 \times 0.7771$$

Step4: Compute final value and round

$$161.5 \times 0.7771 \approx 125.5$$

Answer:

125.5 square units