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3 years ago

What is the length of CD

Mathematics

2 answers:

fgiga [73]3 years ago

3 0

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.

faltersainse [42]3 years ago

3 0

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.

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