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navik [9.2K]
3 years ago
13

An isosceles triangle has slant height s and angle t opposite the base. Find a formula for the base length b in terms of the ang

le t and the slant height s.Find a formula for the enclosed area A in terms of t and s.
Mathematics
1 answer:
Mars2501 [29]3 years ago
7 0

OK, let's try with no figure.  We have an isosceles triangle sides s,s, and b.

Opposite b is angle t.

Draw the altitude h to bisect t.  We have two right triangles, legs b/2 and h, hypotenuse s.  The angle opposite b/2 is t/2 so

sin(t/2) = (b/2)/s = b/2s

So we arrived at the first part,

b = 2s sin(t/2)

The area of a triangle with sides s,s and included angle t is

A = (1/2) s² sin t

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