SOLUTION: the base of an isosceles triangle is 20cm and the angle opposite the base is 84 degree, find a)equal side b) altitude c) perimeter d) total atea of the isosceles triangle.

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Question 970204: the base of an isosceles triangle is 20cm and the angle opposite the base is 84 degree, find a)equal side b) altitude c) perimeter d) total atea of the isosceles triangle.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!


The altitude from tip to the middle of the base cuts base into two segments of 10 cm each, and the tip angle into two angles of 42 degrees each, and forms two congruent right triangles.

Let the altitude size be the number, a.

10%2Fa=tan%2842%29

a%2F10=1%2Ftan%2842%29

highlight%28a=10%2Ftan%2842%29%29-------now the altitude is known.

The area of the isosceles triangle: highlight%28%281%2F2%29%2820%29%2A10%2Ftan%2842%29%29, and you can handle the simplification any way you want or need.

Either of the equal sides:
Let h be a number for the hypotenuse of either of the right triangles, same as either of the equal sides of the isosceles triangle.

10%2Fh=sin%2842%29

h%2F10=1%2Fsin%2842%29

highlight%28h=10%2Fsin%2842%29%29-----either equal side of the isosceles triangle.
Simplify into whatever you need or want.