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3 years ago

Set up the equations to determine s and t.

Mathematics

1 answer:

Viefleur [7K]3 years ago

5 0

Answer:

t° = 11° s°= 71°

Step-by-step explanation:

79° + t° =90° (Given)

t°= 90° - 79°

t°= 11°

s°+79°+11°+19° =180° (angles on an str line)

s° = 180° - 109°

s° = 71°

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Question:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Answer:

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Step-by-step explanation:

Given

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$

Required

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$tan(30^{\circ}) = \frac{1}{\sqrt{3}}$

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$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}$

Simplify the denominator

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$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}$

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}$

Express the fraction as:

$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{2}{\sqrt 3} / \frac{4}{3}$

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$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{3}{2\sqrt 3}$

Rationalize

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$\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}$ $= \frac{\sqrt{3}}{2}$

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