Question

Consider the diagram below.

Determine the values of a,b, and c.



How do I solve this?

Answer 1

a ≈ 664.47

b ≈ 502.29

c ≈ 767.27

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