The problem shows a triangle with an area of 26 m², one side labeled 13 m, an angle of 30°, and another side $x$ that we need to find. To solve for $x$, we can use the formula for the area of a triangle involving two sides and the sine of the included angle:

$\text{Area} = \frac{1}{2}ab \sin(C)$

Where:

• $a = 13$ m (the known side),
• $b = x$ (the unknown side),
• $C = 30^\circ$ (the included angle),
• Area = 26 m².

Substitute the known values into the formula:

$26 = \frac{1}{2} \times 13 \times x \times \sin(30^\circ)$

We know that $\sin(30^\circ) = 0.5$, so:

$26 = \frac{1}{2} \times 13 \times x \times 0.5$

Simplify the equation:

$26 = \frac{13x}{4}$

Multiply both sides by 4 to eliminate the denominator:

$104 = 13x$

Solve for $x$:

$x = \frac{104}{13} = 8 \, \text{m}$

Thus, the length of $x$ is 8 m.

Would you like more details or have any questions?

Related Questions:

1. How would the solution change if the angle were different?
2. What if the area of the triangle were larger, like 40 m²?
3. How is the sine rule different from the area formula used here?
4. Can this method be used for non-right triangles?
5. How do you derive the formula for the area of a triangle using trigonometry?

Tip:

Always double-check if you are working with degrees or radians when using trigonometric functions.