Let the lengths of CB be a, BA be c, CA be b, CD be d, and DA be e.

Then:

1. In triangle DBC, d / a = sin(DBC)

2. Angle DBC = 90deg – angle BCA (sum of angles of BCD)

3. In triangle ABC, a / c = sin(CAB)

4. Angle CAB = 90deg – angle BCA (sum of angles of ABC)

5. From 2 and 4, angle DBC = angle CAB.

6. From 1, 3 and 5, d / a = a / c.

7. Multiiplying equation 6 by ac: cd = a^2.

8. Similarly from triangles BAD and ABC it follows that:

ae = c^2.

Height of kite = 30sin(52deg) = 23.64ft.

USE YOUR SCIENTIFIC CALCU

sin(52degrees) = height of kite / hypotenuse

sin(52degrees) = height of kite / 30

height of kite = sin(52degrees) * 30

NOW GET YOUR CALCU and do “sin(52degrees) * 30”

I hope you know how to use the “sin” button.