Suppose a triangular silk scarf has both of its shortest sides 14 inches long. If the angle between these sides is 110 degrees, what is the area of the scarf?
Stacey Warren - Expert brainly.com
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Thank's for the welcome!
just clear this up, two sides of a triangle is 14?
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The question doesn't give a picture, so I suppose so.
so youre looking for a base
any missing side of a triangle will be less than the sum and greater than the difference of the other two sides
so what are you saying?
sorry the problem can be done in a different way.
Since we know two of the sides are 14 inches long, you need to find the other side so you can find out the area.Since it is an isosceles triangle, this means the other two angles will both be equal. Since there is an 110 degree angle we know about, this means the other two are (180-110)/2 = 70/2 = 35 degrees each.
an angle bisector can be drawn down from the 110 angle, which will split the triangle into two congruent triangles with angles 55, 35, and 90.
Now all we have to do now is just simple right trigonometry to find the length of the legs (which will be the height and base of the original triangle).
To find the first side (which is the vertical side), we have:
sin(35) = opp/hyp = x/14
sin(35) = x/14
14*sin(35) = x
To find the other side, which is the horizontal side (half of the base of the original triangle), we have:
cos(35) = adj/hyp = x/14
cos(35) = x/14
14*cos(35) = x
x = 11.5
So we have 8 for our height and 11.5 for HALF of our base- which would be 23.
Area of a triangle = 1/2*b*h = (1/2)*8*23 = 4*23 = 92
The scarf has an approximate area of 92 square inches.