Question

URGENT,FIGURE IN PHOTO,
what is -
1.Angle ABC
2.Angle OCD
3.Angle DAC
4.Distance between AB

Answer 1

Answer:

1. angle ABC is 90°

2. angle OCD is 60°

3. angle DAC is 30°

4. Distance between AB is 15√3 units.

Step-by-step explanation:

1. Angle in semicircle is right angle.

2. since OC and OD are radius OC = OD. Also given that OC = CD. consider ∆ OCD we have

OC = OD = CD implies that equilateral triangle. all the angles are equal. so Angle OCD = 60°.

3. Angle ADC = 90° since sum of the opposite angles are supplementary.

since ODC = 60° we have angle ADO + ODC = 90

then ADO = 90 - 60 = 30

Also OA = OD since it is radius.

consider AOD is a triangle in that two sides OA = OD then ∆AOD is a isosceles triangle.

In isosceles triangle, angles in the opposite sides are equal.

Angle DAC = angle DAO = 30°.

4. Consider triangle ∆ADC is right angled triangle. we have AC² = AD² + CD²

since DC equals 15 cm we have

30² = AD² + 15²

AD² = 30² - 15²

= 900 - 225

= 675

AD = 15√3. since given that AB = AD.

then AB = 15√3 units.