To solve the right triangle, we are given the following information:
Side a = 3-√3
Side b = 1
Angle A = 30°
We can use the trigonometric ratios sine, cosine, and tangent to find the missing sides and angles of the triangle.
1. Find angle B:
Since angle A is 30°, angle B is 90° (as it is a right triangle). Therefore, angle C = 180° - angle A - angle B = 180° - 30° - 90° = 60°.
2. Find side c:
We can use the sine ratio to find side c:
sin(A) = opposite/hypotenuse
sin(30°) = a/c
c = a/sin(30°) = (3-√3) / sin(30°)
3. Simplify side c:
To simplify side c, we need to rationalize the denominator.
We know that sin(30°) = 1/2, so c = (3-√3) / (1/2) = 2(3-√3) = 6-2√3
4. Find side d:
We can use the cosine ratio to find side d:
cos(A) = adjacent/hypotenuse
cos(30°) = b/d
d = b/cos(30°) = 1 / cos(30°)
5. Simplify side d:
To simplify side d, we need to rationalize the denominator.
We know that cos(30°) = √3/2, so d = 1 / (√3/2) = 2/√3 = (2√3) / 3
Therefore, the lengths of the sides of the right triangle are:
a = 3-√3
b = 1
c = 6-2√3
d = (2√3) / 3