Question

AB is a vertical pole and C is the middle point on the level ground and P is any point on the level ground other than A.
The portion CB subtends an Angle $\beta$ at P
If AP : AB = 2 : 1 then Find Value of $\beta$
​

Answer 1

Step-by-step explanation:

Given,

AP : AB = 2 : 1

∠CPB = β

Solution :-

Let,

∠APC be 'α'

According to question :-

'C' is mid-point of line segment AB :-

→ AC : CB = 1 : 1

Let, AC = CB = a

→ AB = AC + CB

= a + a

= 2a

AP : AB = 2 : 1

Cross multiplying :-

1(AP) = 2(AB)

AP = 2AB

AP = 2(2a)

AP = 4a

Finding value of 'tanα' :-

tanα = opposite side/adjacent side

= CA/AP

= a/4a

= 1/4

Finding value of tan(α + β) :-

tan(α + β) = opposite side /adjacent side

tanα + tanβ/1 - tanα tanβ = AB/AP

1/4 + tanβ / 1 - (1/4)(tanβ) = 2a/4a

1 + 4tanβ/4/1 - tanβ/4 = 1/2

1 + 4tanβ/4 × 1/1 - tanβ/4 = 1/2

1 + 4tanβ/4 × 1/4 - tanβ/4 = 1/2

1 + 4tanβ/4 × 4/4 - tanβ = 1/2

1 + 4tanβ/4 - tanβ = 1/2

2(1 + 4tanβ) = 1(4 - tanβ)

2 + 8tanβ = 4 - tanβ

9tanβ = 2

tanβ = 2/9

$\beta = tan^{ - 1} \left( \dfrac{2}{9} \right)$

Used formula :-

tanA = opposite side/adjacent side

tan(A + B) = tanA + tanB/1 - tanAtanB

Note : Refer to above picture

Answer 2

★QUESTION:-

AB is a vertical pole and C is the middle point on the level ground and P is any point on the level ground other than A.The portion CB subtends an Angle beta at P If AP : AB = 2 : 1 then Find Value of beta.

★ANSWER:-

B = tan ^ -1 ( 2/9)

★REFER THE ATTACHMENT FOR EXPLANATION