Find the perpendicular distance from C to AB and area of the triangle

To Find The Perpendicular Distance From C to AB :

Tan60° = CD/AD

=> √3 = CD/AD
=> AD = CD/√3 ……….(1)

Tan45° = CD/DB

=> 1 = CD/DB
=> 1 = CD/(10-AD)
=> 10-AD = CD
=> AD = 10- CD ………(2)

=> By (1) & (2)

CD/ √3 = 10-CD
=> CD = 10√3 - √3CD
=> CD +√3CD = 10√3
= CD(1+√3) = 10√3
=> CD = 10√3 / (1+√3)
= CD = {10√3( 1-√3)} / {(1+√3)(1-√3)}
= CD = (10√3 - 30) / -2
=> CD = (30–10√3) / 2
=> CD = 15 - 5√3
=> CD = 15 - 5 ×1.732
=> CD = 15- 8.66

= CD = 6.36 cm ( approx)

Area of the Triangle :

= 1/2 × Base × Height
= 1/2 × 10 × 6.36
= 31.8 cm²