Question

Two poles standing on a horizontal ground are of heights 5m and 10 m respectively. The line joining their tops makes an angle of 15º with ground. Then the distance (in m) between the poles, is
(A) (5/2)(2 + √3)
(B) 5(√3 + 1)
(C) 5(2 + √3) (D) 10(√3 - 1)

Answer 1

Answer:

hope it will help you mate and thanks

Answer 2

Answer:

(C) 5(2 + √3)

Step-by-step explanation:

tan15°=tan(45°-30°)

This gives:

=(tan 45°-tan30°)/(1+tan45°xtan30°)

This gives;

=[{1-(1/√3)}/{1+(1)(1/√3)}]

Which simplifies to

=(√3–1)/(√3+1)

When we rationalizing the denominator, we get:

Tan15°= {(√3–1)×(√3–1)}/{(√3+1)×(√3–1)}

 Simplify

=(3+1–2√3)/(3–1)

 

Giving

=(4–2√3)/2

So, tan 15

=2-√3

From the attached diagram, AD is the required distance

Tan 15 = 5/AD

2-√3 = 5/AD

AD = 5/ (2-√3)

Rationalize the denominator:

AD = 5(2+√3)

The correct answer is choice C