Solve the right triangle, while a= 10; find B, b and c.

Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180 for β
β = 180° - (90 + 50)° = 180° - 140° = 40°
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tan50° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{10}{b}[/tex]
Multiply both sides by b
b × tan50° = 10 ( divide both sides by tan50° )
b = [tex]\frac{10}{tan50}[/tex] ≈ 8.39 ( to 2 dec. places )
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sin50° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{c}[/tex]
Multiply both sides by c
c × sin50° = 10 ( divide both sides by sin50° )
c = [tex]\frac{10}{sin50}[/tex] ≈ 13.05 ( to 2 dec. places )
Answer:
<b=40
Step-by-step explanation:
<b=180-(90+50) - (sum of all the angles of a triangle is 180)
=180-140
<b=40