SOLUTION: I have a triangle, it is an isoceles (I think i spelled that wrong). I know it is isoceles because it has a base then, the two sides are marked congruent. I have the degree measure

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Question 308413: I have a triangle, it is an isoceles (I think i spelled that wrong). I know it is isoceles because it has a base then, the two sides are marked congruent. I have the degree measure of one angle, its 70 degrees. So, i found out the other degree angles are 70, and 30. It gives me the base length, 10. I need to find the area. I know to find the area, I need to find the height. (A= 1/2 bh) That's where I got stuck. How do I do this problem? Thank you.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Couple of things.
You did spell isoceles correctly.
However your angle is off.
The sum of the angles of a triange equal 180.
70%2B70%2BA=180
A=180-140
A=40
So the angle is 40 degrees, not 30.
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.
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If you drop a line from the 40 degree vertex that bisects the base you then create two right triangles from your isoceles triangle.
From trig, you know that
tan%2870%29=OPP%2FADJ
In your case,
ADJ=%281%2F2%29%2810%29=5
OPP=h
which is the height you need for the area equation.
SO then,
h=5%2Atan%2870%29
and the area is then,
A=%281%2F2%29%285%29%2A5%2Atan%2870%29
This is the area of the right triangle.
Double it to get the area of the isoceles triangle.
Ai=2%281%2F2%2925%2Atan%2870%29
Ai=25%2Atan%2870%29 or approximately
Ai=68.7 sq. units.