In ΔHIJ, h = 730 cm, i = 390 cm and ∠J=35°. Find the area of ΔHIJ, to the nearest square centimeter.
To find the area of ΔHIJ, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
First, we need to find the base of the triangle. We know that i and h are the sides of the triangle adjacent to angleJ. We can use the cosine rule to find the length of side ij:
ij^2 = i^2 + h^2 - 2ih * cosJ
ij^2 = 390^2 + 730^2 - 2(390)(730) * cos35°
ij^2 ≈ 244122.51
ij ≈ √244122.51
ij ≈ 494.06 cm
Now we can calculate the area of the triangle:
Area = (1/2) * ij * h
Area = (1/2) * 494.06 * 730
Area ≈ 180424.140 cm^2
Therefore, the area of ΔHIJ to the nearest square centimeter is 180424 cm^2.