Question

Find the length of AC. Use that length to find the length of CD. What is the length of CD? Round to the nearest tenth.

A) 2.3 cm
B) 4.0 cm
C) 10.7 cm
D) 18.6 cm

Answer 1

Find out the what is the length of CD , AC .

To prove

By using the trignometric identity

`sin B = (Perpendicular)/(Hypotenuse)`

As in ΔABC

∠ B = 30° , AB= 10 cm

put in the trignometric identity

`sin 30^(\circ) = (AC)/(10)`

As

`sin30^(\circ) =(1)/(2)`

`(1)/(2) = (AC)/(10)`

`AC = (10)/(2)`

AC = 5cm

Now in the ΔADC

`tan D^(\circ) = (Perpendicular)/(Base)`

∠ D = 25° , AC = Perpendicular = 5 cm

`tan 25^(\circ) = (5)/(CD)`

tan 25 ° = 0.46630765815 (approx)

`CD = (5)/(0.46630765815)`

CD = 10 .7cm ( approx )

Option (C) is correct .

Answer 2

length of AC = 10 * sin(30) = 5 cm

Length of CD = 5 /tan(25) = 10.7cm

answer is C