Question

If c = 10 then the value of a is…

Answer 1

Last option

Explanation:

cos30° = a/10

a = 10cos30°

`cos30=0.8660=(√(3) )/(2)`

`a=10((√(3) )/(2) )=5√(3)`

Hope this helps

Answer 2

5
`√(3)`

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
  `√(3)`

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.

• 10/2 = 5

Thus, b = 5

Next, plug this value into the formula for b

• a = 5
  `√(3)`