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

Answer:

Option C. 56 cm

Step-by-step explanation:

From the diagram attached, in ΔABC

By Pythagoras Theorem,

AB² = AC² + BC²

      = 16² + 30²

      = 256 +900

AB² = 1156

AB  =  34

Now sinA = $\frac{BC}{AB}$ = $\frac{30}{34}$

             A = sin⁻¹  $(\frac{30}{34})$ = 61.93°

From ΔABD

∠A + ∠B + ∠D = 180°

61.93° + 90° + ∠D = 180°

∠D = 180 - 151.93° = 28.07°

Now tan 28.07° =$\frac{BC}{CD}$ = $\frac{30}{CD}$

0.53328=$\frac{30}{CD}$

CD = $\frac{30}{0.53328}$ = 56.25 cm ≈ 56 cm

Option C. 56 cm is the answer.