Answer:
5[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Special right triangles, such as the one shown, have unique equations that can be used to find missing sides.
30-60-90 Triangles
The angle measurements show us that this is a 30-60-90 triangle. This name refers to the 3 angle measurement. There are 2 types of special right triangles, 45-45-90 and 30-60-90. For most triangles, it would take the law of sine or cosine to find a missing side with only 1 side given. But, with special right triangles, we can use shortcuts to find a.
Formulas
For all 30-60-90 triangles, there are 3 sides: the hypotenuse (c), the long leg (a), and the short leg (b). The shortcuts for 30-60-90 triangles are based on the length of the short leg.
The formulas are as follows (the variables match the variable given in the figure):
- c = 2b
- b = 0.5c
- a = b[tex]\sqrt{3}[/tex]
Solving for a
So, to find a, we must first find b. Since b is equal to half of c, we can divide the value of c by 2.
Thus, b = 5
Next, plug this value into the formula for b
