How to find gradient with given acute angle? (full question in photo)

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Answer 1 · 2018-07-11T09:34:44

# b=-1/2, or, b=8#.

Suppose that the given lines

#l_1 : 3x-5y-1=0 and l_2 : bx-2y+2# have gradients

#m_1 and m_2#, resp.

Then, #m_1=3/5, and, m_2=b/2#.

So, if #/_(l_1,l_2)=alpha, tanalpha=|(m_1-m_2)/(1+m_1m_2)|#.

#:. tan45^@=|(3/5-b/2)/(1+(3/5)(b/2))|#.

#:. |(6-5b)/(10+3b)|=1#.

#:. (6-5b)/(10+3b)=+1, or, (6-5b)/(10+3b)=-1#.

#:. 6-5b=10+3b, or, 6-5b=-10-3b#.

#:. -8b=+4, or, -2b=-16#.

# rArr b=-1/2, or, b=8#.