How do I find the mesurements of a isosceles triangle? I have the sides set as E=72 degrees, and the legs that come down are 15, and i have to find D and F..I have no clue how to do this. Or any idea of a formula to help with this.
The two base angles are equal, and the sum of the three angles is 180. Now for the sides, I am not certain what you mean by legs. If you mean the two equal sides of the triangle, then you can use the law of cosines or law of cosines to find the other side.
The two base angles are equal, and the sum of the three angles is 180. Now for the sides, I am not certain what you mean by legs. If you mean the two equal sides of the triangle, then you can use the law of cosines or law of cosines to find the other side.
why don't u just ask 4 a way 2 work it out with height and base measurements
To find the measurements of an isosceles triangle given that one angle is 72 degrees and the equal sides are 15 units long, you can use the properties of isosceles triangles and basic trigonometry.
First, let's label the triangle as follows:
- The base angles are A and B.
- The unequal side is labeled as c.
- The equal sides are labeled as a and b, with a = b = 15.
Since the sum of the angles in any triangle is 180 degrees, and we know that one angle is 72 degrees, we can find the measure of the other base angle by subtracting 72 from 180 and dividing the result by 2. So, both base angles A and B would have a measure of (180 - 72)/2 = 54 degrees.
Now, to find the remaining side c, which is opposite the 72-degree angle, we can use the law of cosines:
c^2 = a^2 + b^2 - 2ab * cos(C),
where C is the angle opposite side c. Since we know that the two equal sides a and b have a length of 15 units, and C is 72 degrees, we can plug in these values to calculate c:
c^2 = 15^2 + 15^2 - 2(15)(15) * cos(72).
Simplifying the equation gives:
c^2 = 450 + 450 - 450 * cos(72),
c^2 = 900 - 450 * cos(72).
Now, you can use a calculator to find the value of cos(72) and compute the value of c.
To find the remaining angles D and F, we know that they must be equal since the triangle is isosceles. Let's call them both x degrees. Since the sum of the angles in any triangle is 180 degrees, we can set up the following equation:
D + F + E = 180.
By substituting the known values, we have:
x + x + 72 = 180,
2x + 72 = 180,
2x = 180 - 72,
2x = 108.
Solving for x gives:
x = 108 / 2,
x = 54.
Therefore, both angles D and F have a measure of 54 degrees.
In summary:
- Angle A = Angle B = 54 degrees,
- Angle C = 72 degrees,
- Angle D = Angle F = 54 degrees,
- Side a = Side b = 15 units,
- Side c can be calculated using the law of cosines.
Please note that without further information, this is the best you can determine about the isosceles triangle based on the given data.