Question

if the slope of a line passing through the points (2,5) and (5, 8) is represented by tan theta
then find theta ( 0<theta<90 )​

Answer 1

$\LARGE{\underline{\bf{Required\: Answer :}}}$

The coordinates of points:

• (2, 5)
• (5, 8)

The slope is represented by tan theta.

We have to find:

• Value of theta?

Step-by-step explanation:

We know that,

The slope of a straight line can be expressed as tan Θ. Here slope means how much the line is inclined to the horizontal axis i.e. x axis.

Also,

Slope = Difference of y coordinates / Difference of x coordinates

Then,

• Difference of Y coordinates = 8 - 5 = 3
• Difference of X coordinates = 5 - 2 = 3

Therefore

⇒ Slope = 3 / 3 = 1

That means,

⇒ tan Θ = 1

because the slope is also given by tan Θ

And we know that,

The value of tan Θ is 1 when Θ = 45°. Hence, the measure of Θ or the angle with which it is inclined is:

$\huge{ \boxed{ \sf{ \purple{45 \degree}}}}$

Answer 2

Answer:

$\huge \bf \: required \: answer$

Co-ordinate of line

(2,5)

(5,8)

Now as we know that

$\sf \: slope \: = \frac{difference \: of \: y}{difference \: of \: x}$

$\sf \: slope \: = \frac{8 - 5}{5 - 2}$

$\sf \: slope \: = \frac{3}{3} = 1$

Now, it is given that the line is represented as tan theta

So,

As we know that tan theta = 45⁰

$\sf \therefore \: slope \: 45 \degree$

Extra shots

The value of tan Θ is 1 when Θ = 45°. Hence, the measure of Θ is 45⁰