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3 years ago

Help asap will mark BRAINLIEST

Mathematics

1 answer:

dsp733 years ago

4 0

x = 81 degrees (The sum of a triangle's angles must be 180 degrees. 48 + 51 = 99, and 180 - 99 = 81)

y = 99 degrees (Y and X are on a supplementary angle. Like a triangle, a supplementary angle's angles must add up to 180 degrees. 180 - 81 = 99)

z = 129 degrees (Z and the 51 degree angle are also on a vertical angle. 180 - 51 = 129)

Hope this helps!

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For this problem, we are going to use the <em>law of sines</em>, which states:

$\dfrac{\sin{A}}{a} = \dfrac{\sin{B}}{b} = \dfrac{\sin{C}}{c}$

In this case, we have an angle and two sides, and we are trying to look for the third side. First, we have to find the angle which corresponds with the second side, $B$ . Then, we can find the third side. Using the law of sines, we can find:

$\dfrac{\sin{39^{\circ}}}{11} = \dfrac{\sin{B}}{13}$

We can use this to solve for $B$ :

$13 \cdot \dfrac{\sin{39^{\circ}}}{11} = \sin{B}$

$B = \sin^{-1}{\Big(13 \cdot \dfrac{\sin{39^{\circ}}}{11}\Big)} \approx 48.1$

Now, we can find $C$ :

$C = 180^{\circ} - 48.1^{\circ} - 39^{\circ} = 92.9^{\circ}$

Using this, we can find $c$ :

$\dfrac{\sin{39^{\circ}}}{11} = \dfrac{\sin{92.9^{\circ}}}{c}$

$c = \dfrac{11\sin{92.9^{\circ}}}{\sin{39^{\circ}}} \approx \boxed{17.5}$

c is approximately 17.5.

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