Respuesta :

gmany

Answer:

[tex]\huge\boxed{\tan\theta=\dfrac{\sqrt{39}}{5}\approx1.25}[/tex]

Step-by-step explanation:

[tex]tangent=\dfrac{opposite}{adjacent}\\\\\text{We have}\ adjacent=5,\ hypotenuse=8.\\\\\text{Find the opposite using Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{Substitute}\ leg=5,\ leg=x,\ hypotenuse=8\\\\5^2+c^2=8^2\\\\25+x^2=64\qquad\text{substitute 25 from both sides}\\\\25-25+x^2=64-25\\\\x^2=39\to x=\sqrt{39}\\\\\text{Calculate tangent}[/tex]

[tex]\tan\theta=\dfrac{\sqrt{39}}{5}[/tex]

altavistard

Answer:

√39 / 5

Step-by-step explanation:

Find Tan Ф where Ф is the angle shown.

Since the tangent function is defined as opp side / adj side, we'll need to find the length of the opp (vertical) side to answer this question.

We do this through use of the Pythagorean Theorem:

8² = opp² + 5², or 64 = opp² + 25.  Then opp² = 64 - 25 = 39, and

opp = √39.

Then the tangent of the angle shown is

           

             opp       √39

tan Ф = -------- = --------

              adj           5

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