Answer:
b = 3.5
a = 7
Step-by-step explanation:
Hello!
This triangle is a 30°-60°-90° triangle, as the missing angle is 30° and the other two angles are 60° and 90°.
There are some important Rules:
- The leg that is opposite to the 30° angle is half of the hypotenuse.
- The leg that is opposite to the 60° angle is the length of the leg opposite to the 30° multiplied by [tex]\sqrt3[/tex].
We can first solve for the leg that is opposite to the 30° angle.
Since [tex]\frac{7\sqrt3}{2}[/tex] is [tex]b\sqrt3[/tex]:
- [tex]\frac{7\sqrt3}{2} = b\sqrt3[/tex]
- [tex]\frac72 = b[/tex]
The length of b is 3.5.
We can multiply 3.5 by 2 to find the length of a.
- [tex]\frac a2 = b[/tex]
- [tex]\frac a2 = \frac72[/tex]
- [tex]a = 7[/tex]
The length of a is 7.
