The hypotenuse of a right triangle measures 9 inches, and one of the acute angles measures 36 degrees. What is the area of the triangle?

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Answer 1 · 2018-03-24T05:57:36

#color(blue)("Area of right triangle " A_t ~~ 19.26 " sq units"#

www.commons.wikimedia.org/wiki/File:Triangulo_rectangulo.PNG

#"Given : " beta = 36^@, c = 9#"

#alpha = = 180 - 90 - 36 = 54^@#

According to Law of sines,

#:. a / sin beta = b / sin alpha = c / sin (90^@)#

#a = (c * sin beta) / sin 90 = 9 sin 36^@ = 5.29#

#b = (c * sin alpha) / sin 90 = 9 * sin 54^@ = 7.28#

#"Area of right triangle " A_t = (1/2) a b = 0.5 * 5.29 * 7.28 ~~ 19.26#