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2 years ago

60° Х 48° 72° X- degrees

Mathematics

2 answers:

lbvjy [14]2 years ago

7 0

Answer:

x=132

Step-by-step explanation:

Hey There!

The angle that is equal to 48 and angle x are supplementary angles meaning that they will add up to equal 180

so to find x we subtract 48 from 180

180-48=132

therefore x=132

eimsori [14]2 years ago

5 0

Answer:

132

Step-by-step explanation:

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

x = 60° + 72°

x = 132°

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motikmotik

Given:

There are given that the cos function:

$cos210^{\circ}=-\frac{\sqrt{3}}{2}$

Explanation:

To find the value, first, we need to use the half-angle formula:

So,

From the half-angle formula:

$cos(\frac{\theta}{2})=\pm\sqrt{\frac{1+cos\theta}{2}}$

Then,

Since 105 degrees is the 2nd quadrant so cosine is negative

Then,

By the formula:

$\begin{gathered} cos(105^{\circ})=cos(\frac{210^{\circ}}{2}) \\ =-\sqrt{\frac{1+cos(210)}{2}} \end{gathered}$

Then,

Put the value of cos210 degrees into the above function:

So,

$\begin{gathered} cos(105^{\circ})=-\sqrt{\frac{1+cos(210)}{2}} \\ cos(105^{\operatorname{\circ}})=-\sqrt{\frac{1-\frac{\sqrt{3}}{2}}{2}} \\ cos(105^{\circ})=-\sqrt{\frac{2-\sqrt{3}}{4}} \\ cos(105^{\circ})=-\frac{\sqrt{2-\sqrt{3}}}{2} \end{gathered}$

Final answer:

Hence, the value of the cos(105) is shown below:

$cos(105^{\operatorname{\circ}})=-\frac{\sqrt{2-\sqrt{3}}}{2}$

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