The sine and cosine of one of the acute angles in a right triangle are equal. What is the tangent of the angle?

Mathematics

1 answer:

Gnoma [55]4 years ago

4 0

Answer:

Step-by-step explanation:

Since tan(x) = sin(x)/cos(x), if sin(x) = cos(x) then tan(x) must be 1.

You can even reason that the acute angle is 45° and sin(x)=cos(x) = $\frac12\sqrt2$ .

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a group of astronauts launched a model rocket from a platform. Its flight path is modeled by h= -4t^2+24t+13 where h is the heig

Eddi Din [679]

Answer:

6.5 seconds

Step-by-step explanation:

Keep in mind that when $h=0$ , this is the same height for both when the model rocket takes off and lands, so when the rocket lands, time is positive. Thus:

$h=-4t^2+24t+13\\\\0=-4t^2+24t+13\\\\t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\t=\frac{-24\pm\sqrt{24^2-4(-4)(13)}}{2(-4)}\\ \\t=\frac{-24\pm\sqrt{576+208}}{-8}\\\\t=\frac{-24\pm\sqrt{576+208}}{-8}\\\\t=\frac{-24\pm\sqrt{784}}{-8}\\\\t=\frac{-24\pm28}{-8}\\\\t=\frac{-24-28}{-8}\\ \\t=\frac{-52}{-8}\\ \\t=\frac{52}{8}\\\\t=6.5$