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

Answer:

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■Slope(m) lines is given by:

$= > m = \frac{y2 - y1}{x2 - x1}$

■Here we have two points

• ☞ (2,5)→À (say)
• ☞ (5,8)→B (say)

■From these two points we got:

• x1=2 & x2=5
• y1=5 & y2=8

Therefore:-

Putting the values, we get:

$= > m = \frac{8 - 5}{5 - 2}$

$= > m = \frac{3}{3}$

$= > m = 1$

■Now:

As we know, slope(m) of given lines is tanθ

Therefore:-

$= > m = tanθ$

$= > 1 = tanθ$

$= > tan {45}^{0} = tanθ$

$= > θ = {45}^{0}$

Therefore the value of tanθ is 45⁰

Hope it helps!

Answer 2

Slope(m) lines is given by:

= > m = \frac{y2 - y1}{x2 - x1}=>m=

x2−x1

y2−y1

■Here we have two points

☞ (2,5)→À (say)

☞ (5,8)→B (say)

■From these two points we got:

x1=2 & x2=5

y1=5 & y2=8

Therefore:-

Putting the values, we get:

= > m = \frac{8 - 5}{5 - 2}=>m=

5−2

8−5

= > m = \frac{3}{3}=>m=

3

3

= > m = 1=>m=1

■Now:

As we know, slope(m) of given lines is tanθ

Therefore:-

= > m = tanθ=>m=tanθ

= > 1 = tanθ=>1=tanθ

= > tan {45}^{0} = tanθ=>tan45

0

=tanθ

= > θ = {45}^{0}=>θ=45

0

Therefore the value of tanθ is 45⁰

Hope it helps!

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