The area $A$ of a right-angled triangle can be found using the formula:

$A = \frac{1}{2} \times \text{base} \times \text{height}$

Given:

• $A = 26.56$
• $\text{base} = 8.3$

Let's solve for the height $h$.

Step-by-Step Solution

1. Substitute the values into the area formula:

   $26.56 = \frac{1}{2} \times 8.3 \times h$

2. Multiply both sides by 2 to eliminate the fraction:

   $2 \times 26.56 = 8.3 \times h$

   $53.12 = 8.3 \times h$

3. Now, divide both sides by 8.3 to solve for $h$:

   $h = \frac{53.12}{8.3}$

4. Calculating this gives:

   $h \approx 6.4$

Answer

The height of the triangle is approximately 6.4 units.

Would you like further details or have any questions?

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Here are five related questions for further practice:

1. If the base and height of a triangle are both increased by a factor of 2, how does the area change?
2. If the base of a right-angled triangle is halved and the area remains the same, what happens to the height?
3. For a triangle with an area of 50 and a height of 10, what is the base?
4. How would you find the hypotenuse of a right-angled triangle if only the base and area are known?
5. How does changing the base of a triangle affect the height if the area is kept constant?

Tip: Always ensure that the units are consistent when calculating area, especially if given measurements in different units.