Oscar is taking some measurements and is using trigonometry to work out some angles, distances, and areas - Leaving Cert Mathematics - Question 9 - 2022

Since Field 2 shares the same height as Field 1, we can use the following relation for the area of Field 2:

Calculating this:

$ext{Area of Field 2} = 5 imes 26.81 ≈ 134.05 ext{ m}²$

Thus, rounding to the nearest m²:

Area of Field 2 = 134 m²

To find the perimeter of Field 1, we need to calculate the length of |BC| using the cosine rule, as we have two sides and the included angle:

$|BC|^2 = |AB|^2 + |AC|^2 - 2 imes |AB| imes |AC| imes ext{cos}( ext{∠CAB})$

Given that:

• |AB| = 30 m
• |AC| = 35 m

To find |∠CAB|, we first need to know it, or we can assume it is derived from the remaining angle in triangle ABC. However, assuming it is not needed directly:

Calculating, we find:

$|BC|^2 ≈ 30^2 + 35^2 - 2 imes 30 imes 35 imes ext{cos}(50°)$

After finding |BC|, the perimeter can be determined as:

$ext{Perimeter} = |AB| + |AC| + |BC|$

Using the approximation from above, |BC| can be calculated, and finally:

Perimeter of Field 1 = 93 m.