# If the base of an equilateral triangle is 20 feet....?

how long will the top two sides be if the Top angle is 102 degrees OR if it is 110 degrees? Also What will the distance be from the top angle to the middle of the base? ( in both situations. Thanks ! ( When i was in school this would be no problem! )

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In an equilateral triangle, all three angles are 60 degrees. You may be referring to an isosceles triangle where two sides are equal. If the base of the isosceles triangle is 20 feet, then the two equal sides may be calculated using trigonometry. The three angles of a triangle add to 180 degrees. Subtract 102 degrees from 180 degrees to obtain the remaining two angles of the triangle. (180- 102)/2 = 39 degrees. Draw a line from the top angle to the middle of the 20 feet base , then look at the definition of cosine of 39 degrees = adjacent side divided by the hypotenuse. The hypotenuse will be the same as the measurement of the "two top sides." Approximately 13 feet, accurate to two significant figures . For the "top angle" of 110 degrees, the remaining two lower angles must each be 35 degrees (180-110)/2 and the equal sides of the isosceles triangle are 10/cos(35) = 12 feet, accurate to two significant figures.

In the case of 110 degrees, the two "lower angles are 35 degrees (180 - 110)/2 and the two sides of the isosceles triangle are 10 feet/cosine (35 degrees) = 12 feet Accurate to two significant figures.

heights are 7.0 ft and 8.1 ft. (accurate to two significant figures) for top angles of 110 degrees and 102 degrees, respectively.

• What you're describing is an isoseles triangle, not an equilateral one. In an equilateral triangle, the top angle would always be 60 degrees and all the sides equal.

If the top angle is 102, the sides will be 10/sin(51) = 12.9

The altitude would be 10/tan(51) = 8.1

If the top angle is 110, the sides will be 10/sin(55) = 12.2

The altitude would be 10/tan(55) = 7

• a) Triangle with angles 102° & 39° & 39°:

side = 10feet/cos39°

altitude = 10feet*tan39°

b) Triangle with angles 110° & 35° & 35°:

side = 10feet/cos35°

altitude = 10feet*tan35°