Question

Find the length of . Use that length to find the length of .

Answer 1

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

$sin(30)=\frac{AC}{10}$

$AC=10sin(30)$

$AC=5$

now, we can find CD

In triangle ACD , we can use trig

$cot(25)=\frac{CD}{AC}$

$CD=ACcot(25)$

now, we can plug AC=5

$CD=5cot(25)$

$CD=10.7$

Answer 2

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) = $\frac{opposite}{hypotnuse}$.

Sin (30) =  $\frac{AC}{10}$.

Plug the value of sin (30)

$\frac{1}{2}$ = $\frac{AC}{10}$.

On multiplying by 10 both sides

Then AC = 5 cm.

By using AC we will find CD

Cot (theta) =  $\frac{adjecent}{opposite}$.

Cot (25) =  $\frac{CD}{5}$.

2.144 =   $\frac{CD}{5}$.

On multiplying both sides by 5

CD = 10.7 cm

Therefore, AC = 5 cm ,  CD = 10.7 cm.