Suppose triangle ABC is isosceles, with the two equal sides being 10 cm in length and the equal angles being 40 degrees. What is the height and what is the area of the triangle?

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Answer 1 · 2015-11-14T17:13:58

$h = 10 sin 40, A = 50 sin 80$

$B = C = 40º$

$M = (B + C)/2$

$Delta AMC$ is a right triangle $(x, h, 10)$ = (basis, height, hypotenuse)

$sin 40º = h/10$

$cos 40º = x/10$

Area $(Delta ABC) = 1/2 cdot (2x) cdot h = 100 sin 40 cos 40$

We use: $sin 2x = 2 sin x cos x$