Question

Determine the value of x.

Question 11 options:

A)

5

B)

5

C)

10

D)

Answer 1

The value of the side x is 10√3/3. Option C

To determine the value of the side x, we have to make use of the SOHCAHTOA rule which holds for all the ratios of the trigonometric identities.

We have that the trigonometric identities in Mathematics are;

• cosine
• tangent
• cotangent
• sine
• secant
• cosecant

From the diagram, we have that;

Tan 60 = 10/x

find the value and substitute, we have;

√3 = 10/x

cross multiply the values, we get;

x = 10√3/3

Answer 2

Answer:
`(10)/(√(3))`

This is equivalent to
`(10√(3))/(3)`

======================================================

Step-by-step explanation:

To get the first value mentioned above, we simply divide the long leg (10) over the square root of 3.

This is due to the fact that if x is the short leg, then x*sqrt(3) is the long leg. We go in reverse of this process to go from long leg to short leg.

The expression
`(10)/(√(3))` is the same as
`(10√(3))/(3)` after we multiply top and bottom by sqrt(3) to rationalize the denominator.

Side notes:

• This entire process only applies to 30-60-90 triangles.
• The hypotenuse of a 30-60-90 triangle is twice as long as the short leg, so the hypotenuse is
  `2x = 2*(10√(3))/(3) = (20√(3))/(3)` units long.
• You could use the tangent ratio to help isolate x. You would either say tan(30) = x/10 or tan(60) = 10/x as the first equation to set up.