Question

In the adjoining figure exterior 2 EAB = 110°,
2 CAD = 35°, AB = 5cm, AC = 7 cm and
BC = 3 cm. Find CD.​

Answer 1

Answer:

1.5 cm

Step-by-step explanation:

Note: (x) = angle x

Now,

(EAB) + (BAD) + (DAC) = 180 ----- (LINEAR PAIR ANGLE)

110 + X + 35 = 180

X = 35

NOW WE OBSERVE THAT (BAD) AND (DAC) ARE SO SIDE OPPOSITE TO THEM SHOULD ALSO BE EQUAL

SO BD = DC

NOW IT IS GIVEN THAT BC = 3CM

BC = BD + DC

3 = 2Y

Y = 1.5 CM

HENCE CD = 1.5 CM

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Answer 2

Given:

Angle EAB=110°

Angle CAD=35°

AB=5cm, AC=7cm, BC=3cm

To find:

Length of CD

Solution:

The length of the CD is 1.75cm.

We can find the length by following the steps given below-

We know that the angle EAB is exterior to the triangle.

So, angle EAB is equal to the sum of the angle ABC and angle ACB. (Exterior angle property)

So, the sum of angle ABC and angle ACB=110°.

Angle ABC + angle ACB=110° (1)

In ∆ABC, the sum of all the angles will be equal to 180°.

Angle ABC+Angle ACB+Angle BAC=180°

From (1), 110°+ angle BAC=180°

Angle BAC=180°-110°=70°

We know that angle CAD=35°.

From the figure, angle BAC is the sum of angle BAD and CAD.

Angle BAC =angle BAD+ angle CAD

70°=Angle BAD+35°

Angle BAD=70°-35°=35°

This means that AD is the angle bisector.

Since BC=BD+CD and BC=3cm, BD+CD=3

So, BD=3-CD (2)

The angle bisector divides the opposite side in the ratio of the other two sides of the triangle.

So, AB/AC=BD/CD

On putting the values, we get

5/7=BD/CD

From (2),

5/7=(3-CD)/CD

5CD=7(3-CD)

5CD=21-7CD

5CD+7CD=21

12CD=21

CD=7/4

CD=1.75cm

Therefore, the length of the CD is 1.75cm.