Question

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

What is the length of ? Round to the nearest tenth.

2.3 cm
4.0 cm
10.7 cm
18.6 cm

Answer 1

AC = 5 cm , CD = 10.7 cm.

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) =
`(opposite)/(hypotnuse)`.

Sin (30) =
`(AC)/(10)`.

Plug the value of sin (30)

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

On multiplying by 10 both sides

Then AC = 5 cm.

By using AC we will find CD

Cot (theta) =
`(adjecent)/(opposite)`.

Cot (25) =
`(CD)/(5)`.

2.144 =
`(CD)/(5)`.

On multiplying both sides by 5

CD = 10.7 cm

Therefore, AC = 5 cm , CD = 10.7 cm.

Answer 2

Length of CD is 10.7 cm

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)=(AC)/(10)`

`AC=10sin(30)`

`AC=5`

now, we can find CD

In triangle ACD , we can use trig

`cot(25)=(CD)/(AC)`

`CD=ACcot(25)`

now, we can plug AC=5

`CD=5cot(25)`

`CD=10.7`