Answer:
a ≈ 664.47
b ≈ 502.29
c ≈ 767.27
Step-by-step explanation:
The altitude of a right triangle divides it into two smaller, similar triangles. We can prove this by showing that they have the same complementary angles.
We can then find the length of the altitude (b) using similar triangles.
435 / b = b / 580
b² = 252300
b ≈ 502.29
To find a, we can either use Pythagorean theorem, or use similar triangles again.
Using similar triangles:
a / 435 = (435 + 580) / a
a² = 441525
a ≈ 664.47
Using Pythagorean theorem:
a² = b² + 435²
a² = 252300 + 189225
a² = 441525
a ≈ 664.47
Repeating for c:
Using similar triangles:
c / 580 = (435 + 580) / c
c² = 588700
c ≈ 767.27
Using Pythagorean theorem:
c² = b² + 580²
c² = 252300 + 336400
c² = 588700
c ≈ 767.27
