Question

Ab=6cm Ac=12 calculate the lenght of cd

Answer 1

This problem involves the uses of the Pythagorean Theorem as well as the use of Sine.

To start we need to identify what we know and what we don't know. We know that there are two triangles. We are given 2 sides lengths and an angle in one and only an angle in the other. They share one side meaning when we are given 2 sides in one triangle it will be easy to get the third side. What we don't know is the side length of CB DB or CD. We need to find CB in order to find CD.

Pythagorean Theorem for side length CB:

12^2-6^2=√108

√108=10.4 (average)

So CB is equal to 10.4

Sine Calculation for side length CD:

Since we have angle 56* we will use the length we found which will be the opposite side from the angle and then input x for our hypotenuse CD in order to solve.

sin 56* = 10.4/x

sin 56* × x = 10.4/x × x

sin 56*x = 10.4

/sin 56* /sin 56*

x = 12.544....

or 12.6 (average)

So, to conclude, our answer for CD is 12.6cm.

Hope I helped!

Answer 2

12.7 cm

Explanation:

Given information: AB=6cm AC=12cm.

Pythagoras theorem: In a right angle triangle

`hypotenuse^2=base^2+perpendicular^2`

Using Pythagoras in triangle ABC we get

`(AC)^2=(AB)^2+(BC)^2`

`(12)^2=(6)^2+(BC)^2`

`144-36=(BC)^2`

`108=(BC)^2`

Taking square root on both sides.

`√(108)=BC`

Law of sine:

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

Using law of sin we get

`(CD)/(\sin (90))=(√(108))/(\sin (55))`

`(CD)/(1)=(√(108))/(\sin (55))`
`[\because \sin 90^(\circ)=1]`

`CD=12.6866616739`

Approx the data to three significant figures.

`CD\approx 12.7`

Therefore, the length of CD is 12.7 cm.