# In a right-angled triangle ABC, angle C = 90 degrees, AC = 24 cm, BC = 10cm, a perpendicular AD = 18cm

In a right-angled triangle ABC, angle C = 90 degrees, AC = 24 cm, BC = 10cm, a perpendicular AD = 18cm is drawn through point D to the plane, find the inclined DВ and DС.

By the Pythagorean theorem, we find the hypotenuse AB in the triangle given by the condition:
AB = √ (AC² + BC²) = √ (576 + 100) = √676 = 26 (cm).
Consider a right-angled triangle ADC (AD is perpendicular by condition). Find the hypotenuse DC in this triangle:
DC = √ (AD² + AC²) = √ (324 + 576) = √900 = 30 (cm).
Similarly, we consider the right-angled triangle ADB and find the hypotenuse DB:
DB = √ (AD² + AB²) = √ (324 + 676) = √1000 = 31.622776 ≈ 31.6 (cm).
Answer: Length of the oblique DC 30 cm, oblique DB 31.6 cm.

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