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?

1 Answer
sankarankalyanam
Mar 24, 2018

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

Explanation:

![www.commons.wikimedia.org/wiki/File:Triangulo_rectangulo.PNG](useruploads.socratic.org)

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

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

According to Law of sines,

![http://www.mathwarehouse.com/sheets/trigonometry/advanced/law-of-sines-and-cosines/law-of-sines/http://worksheet-with-answer-key.php](https://useruploads.socratic.org/2p3E9snJTMmHpGGHrkAX_law%20of%20sines.jpg)

#:. 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#

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