A missile adjusts its flight path using a triangle formed with height = 7 units and hypotenuse = 25 units. If θ is the angle opposite to height and θ lies in the 1st quadrant, find tan(θ).
\(\dfrac{7}{24}\)
This is a right-angled triangle problem where the height (perpendicular) and hypotenuse are given and we need tan θ.
Given: height (side opposite to θ) = 7 units and hypotenuse = 25 units, with θ in the first quadrant so all ratios are positive.
The unknown side is the base (adjacent side). By the Pythagoras theorem: \(\text{base} = \sqrt{\text{hyp}^2 - \text{height}^2}\).
\(\text{base} = \sqrt{25^2 - 7^2} = \sqrt{625 - 49} = \sqrt{576} = 24\) units.
By definition, \(\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}} = \dfrac{\text{height}}{\text{base}}\).
\(\tan\theta = \dfrac{7}{24}\).
Hence the required value is \(\dfrac{7}{24}\).
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