Question

If the distance between the two points (x, 7) and (sin90°

, 30 cos60°

) is 10.

Find the value of x.​

Answer 1

Answer:

(5sin90,0)=(5×1,0)=(5,0)

Answer 2

Given :

P₁ = (x , 7)

P₂ = (sin90° , 30cos60°)

Distance (d) = 10

To find :

Value of x.

Solution :

sin90° = 1

30cos60° = 30×1/2 = 15

So, P₂ = (1 , 15)

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

$10 = \sqrt{(1-x)^{2} +(15-7)^{2} }$

10² = (1 - x)² + (15 - 7)²

100 = (1 - x)² + 8²

100 = (1 - x)² + 64

(1 - x)² = 100 - 64

(1 - x)² = 36

1 - x = ±6

If we take +6, then

1 - x = 6

x = 1 - 6

x = -5

If we take -6, then

1 - x = -6

x = 1 + 6

x = 7