Question

Find the area of AABC given mZB = 25°, AC = 24, and

BC = 14. Express your answer to 1 decimal place,

Answer 1

To find the area of a triangle given one angle and two sides, use the formula (1/2) × side1 × side2 × sin(angle). For ΔABC with m∠B = 25°, AC = 24, and BC = 14, the area is approximately 35.5 m².

Step-by-step explanation:

To find the area of a triangle (ΔABC) when given an angle and two sides, you can use the formula derived from the sine rule: area = (1/2) × AC × BC × sin(∠B).

Using the given values, the area can be calculated as follows:

1. First, convert the angle measure from degrees to radians if your calculator requires it. Here, the angle ∠B is given as 25°.
2. Next, you can use the formula: area = (1/2) × 24 × 14 × sin(25°).
3. Plugging in the values, we get area = (1/2) × 24 × 14 × sin(25°) = 84 × sin(25°).
4. Using a calculator, you'll find that sin(25°) ≈ 0.4226, so area ≈ 84 × 0.4226, which equals approximately 35.5 m² after rounding to one decimal place.

Therefore, the area of ΔABC is approximately 35.5 m².