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Svetllana [295]
3 years ago
5

Solve the triangle. a = 10, b = 23, C = 95°

Mathematics
1 answer:
gayaneshka [121]3 years ago
3 0
C² = a² + b² - (2ab * cosC) 
<span>c² = 10² + 23² - (2 * 10 * 23 * cos95) </span>
<span>c² = 100 + 529 - (460 * -.08715) </span>
<span>c² = 629 - (-40.1) </span>
<span>c² = 669.1 </span>
<span>c = 25.87 </span>

<span>(Sin C) / C = (Sin A) / A </span>
<span>(Sin 95) / 25.87 = SinA / 10, Remember 0 < A < 85 </span>
<span>(10 * Sin95) / 25.87 = Sin A </span>
<span>A = arcsin ((10 * sin95) / 25.87) </span>
<span>A = 22.65º </span>

<span>B = 180 - A - C </span>
<span>B = 180 - 95 - 22.65 </span>
<span>B = 62.35º </span>

<span>I hope this helps. Have a good day.</span>
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Step-by-step explanation:

Let the first angle be a degrees

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Let the third angle be c degrees

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It is given that sum of the measures of the second and third angles is two times the measure of the first angle.

b+c=2\times a                     ...(ii)

It is given that the third angle is 26 more than the second.

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