How do you solve the right triangle given b = 4, B = 10 degrees?

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Answer 1 · 2018-03-26T10:15:12

#color(brown)(a = 22.69, c = 23.04, hat A = 80^@, A_t = 45.38 " sq units"#

#"it's a right triangle with " b = 4, hat B = 10^@#

![http://blog.cardinalec.com/act-math-finding-an-angle-measure-in-a-right-triangle/]( useruploads.socratic.org )

#hat A = 180 - 90 - 10 = 80^@#

Applying Law of Sines,

#a / sin A = b / sin B = c / sin C#

#a = (b sin A) / sin B = (4 * sin 80) / sin 10 = 22.69#

#c = (b sin C) / sin B = (4 * sin 90) / sin 10 = 23.04#

Verification by applying Pythagoras theorem,

#c = sqrt(a^2 + b^2) = sqrt(22.69^2 + 4^2) = 23.04#

#"Area of the rt triangle " A_t = (1/2) * a * b = (1/2) * 22.69 * 4 = 45.38#