Question

The distance between the points (a cos 25, 0) and (0, a cos65) is _____?

Answer 1

The answer is a.

the sum is according to distance formula

= √(x₂-x₁)²+(y₂-y₁)²

= √(0-a cos 25)² + (a cos 65-0)

= √(a cos 25)² + (a cos  65)²

= √(a cos 25)² + (a sin 25)²

= √(a² cos²25) + (a² sin²25)

= √a²(cos²25 + sin²25)                  we know that  sin²Θ + cos²Θ = 1

= √a²(1)

= √a²

= a

Answer 2

Answer:

a

Step-by-step explanation:

Point A =  (a cos 25, 0)

Point B = (0, a cos65)

We are supposed to find distance between the points

Formula : $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)= (a cos 25, 0)$

$(x_2,y_2)= (0, a cos65)$

Substitute the values in the formula

$d = \sqrt{(0-acos 25)^2+(aCos65 - 0)^2}$

$d = \sqrt{(acos 25)^2+(a Cos65)^2}$

$d = \sqrt{(acos 25)^2+(a Cos(90-65))^2}$

Identity : $cos (90-A)=sin A$

$d = \sqrt{(acos 25)^2+(a sin 25)^2}$

$d = \sqrt{a^2cos^2 25+a^2 sin^2 25}$

$d = \sqrt{a^2(cos^2 25+ sin^2 25)}$

Identity : $sin^2A+Cos^2A =1$

$d = \sqrt{a^2(1)}$

$d = a$

Hence The distance between the points (a cos 25, 0) and (0, a cos65) is a