Question

What is the length of CD

Answer 1

16:30 = 30:x
16x = 900
x = 56.25
so C. is the closest answer
this solution is also know as the geometric mean of the altitude of a right triangle to the parts of the hypotenuse.

Answer 2

Option C. 56 cm

Explanation:

From the diagram attached, in ΔABC

By Pythagoras Theorem,

AB² = AC² + BC²

= 16² + 30²

= 256 +900

AB² = 1156

AB = 34

Now sinA =
`(BC)/(AB)` =
`(30)/(34)`

A = sin⁻¹
`((30)/(34))` = 61.93°

From ΔABD

∠A + ∠B + ∠D = 180°

61.93° + 90° + ∠D = 180°

∠D = 180 - 151.93° = 28.07°

Now tan 28.07° =
`(BC)/(CD)` =
`(30)/(CD)`

0.53328=
`(30)/(CD)`

CD =
`(30)/(0.53328)` = 56.25 cm ≈ 56 cm

Option C. 56 cm is the answer.