Question

the distance between the points ( a cos 25⁰ ,0) and (0,a con 65⁰) is​

Answer 1

Answer:

cos 64⁰

Step-by-step explanation:

cos 63 - by 25

=56⁰

Answer 2

Step-by-step explanation:

Given :-

The points ( a cos 25⁰ ,0) and (0,a cos 65⁰)

To find :-

Find the distance between the given two points?

Solution :-

Given that :

The two points are :

( a cos 25⁰ ,0) and (0,a cos 65⁰)

We know that

Cos (90°-A) = Sin A

Cos 65° = Cos (90°-25°) = Sin 25°

The points (0,a Cos 65° ) = (0, a Sin 25°)

Let (x1, y1) = (a Cos 25⁰,0)

=> x1 = a Cos 25° and y1 = 0

Let (x2, y2) = ( (0, a Sin 25°)

=> x2 = 0 and y2 = a Sin 25°

We know that

The distance between the two points (x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

On Substituting these values in the above formula then

=>D =√[(0-a Cos 25°)²+(a Sin 25°-0)²]

=> Distance =√[(-a Cos 25°)²+(a Sin 25°)²]

=> Distance = √(a² Cos² 25° + a² Sin² 25°)

=> Distance = √[(a²)(Cos² 25° + Sin² 25°)]

=> Distance √[(a²)(Sin² 25° + Cos² 25°)]

We know that

Sin² A + Cos² A = 1

=> Distance = √(a²)(1)

=> Distance =√a²

=> Distance = a units

Answer:-

The distance between the two given points is a units

Used formulae:-

Distance formula:-

The distance between the two points

(x1, y1) and (x2, y2) is √[(x2-x1)²+(y2-y1)²] units

• Cos (90°-A) = Sin A.

• Sin² A + Cos² A = 1