If tan θ + sec θ = 7, θ being acute, then the value of 5 sin θ is:

$\frac{24}{5}$

Given :-

tan θ + sec θ = 7   -----(1)

Then , sec θ - tan θ = \(\frac{1}{7}\)     -----------(2)

Adding equation 1 & 2

2sec θ = 7 + \(\frac{1}{7}\)  = \(\frac{50}{7}\)

sec θ = \(\frac{25}{7}\) 

H = 25 , B = 7

By using pythagoras theorem

P² + B² = H²

P² + 7² = 25²

P = 24

So , 5sinθ = 5 × \(\frac{24}{25}\)  = \(\frac{24}{5}\)