Answer:
Length of CD is 10.7 cm
Step-by-step explanation:
we are given to find length of CD
Calculation of CD:
Firstly, we will find AC
In triangle ABC, we can use trig
[tex]sin(30)=\frac{AC}{10}[/tex]
[tex]AC=10sin(30)[/tex]
[tex]AC=5[/tex]
now, we can find CD
In triangle ACD , we can use trig
[tex]cot(25)=\frac{CD}{AC}[/tex]
[tex]CD=ACcot(25)[/tex]
now, we can plug AC=5
[tex]CD=5cot(25)[/tex]
[tex]CD=10.7[/tex]
Answer:
AC = 5 cm , CD = 10.7 cm.
Step-by-step explanation:
Given : A triangle with a side 10 cm and angle 30 and 25.
To find : Length of AC and CD.
Solution We have given that a triangle
By the trigonometric ratio
Sin ( theta) = [tex]\frac{opposite}{hypotnuse}[/tex].
Sin (30) = [tex]\frac{AC}{10}[/tex].
Plug the value of sin (30)
[tex]\frac{1}{2}[/tex] = [tex]\frac{AC}{10}[/tex].
On multiplying by 10 both sides
Then AC = 5 cm.
By using AC we will find CD
Cot (theta) = [tex]\frac{adjecent}{opposite}[/tex].
Cot (25) = [tex]\frac{CD}{5}[/tex].
2.144 = [tex]\frac{CD}{5}[/tex].
On multiplying both sides by 5
CD = 10.7 cm
Therefore, AC = 5 cm , CD = 10.7 cm.
