In the figure, O is the mid-point of AB and CD, prove that AC = BD

Proved: AC = BD

Step-by-step explanation:

The complete question related to this with diagram can be found at toppr website.

Given: O is the mid point of AB and CD

Find attached the diagram

∠COA = ∠BOD (vertical angles are equal)

∠AOD = ∠COB (vertical angles are equal)

For ∆AOC

AC + OC + OA = 180° (sum of angles in a triangle)

For ∆DOB

DB + OB + OD = 180° (sum of angles in a triangle)

OC = OD (sides are equal)

OA = OB (sides are equal)

Since both ∆AOC and ∆DOB are equal to 180°, AC = DB.

DB = BD

Proved: AC = BD

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225