One of the outer corners of the triangle is 120 degrees. The sum of the hypotenuse and the smaller leg is 15 cm. Find the sides of the triangle.
In a right-angled triangle, the outer angle is 120 °, so the inner angle is 60 °.
The second acute angle will be 90 ° – 60 ° = 30 °.
Let’s denote the hypotenuse for x, then the leg, lying opposite an angle of 30 ° is equal to half of the hypotenuse, that is, x / 2.
x + x / 2 = 15;
3x = 30;
x = 10.
10cm – hypotenuse, smaller leg – 5cm.
Let’s find the second leg according to the Pythagorean theorem: 10^2 = 5^2 + y^2; where y is the second leg.
y^2 = 100 – 25;
y^2 = 75;
y = √75 = 5√3.
Answer: 10cm, 5cm, 5√3cm.
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