Question

5.

15V3
To
Given that the tan 0 = 5V3 and that the side
opposite the angle marked O is 15v3 units long,
what is the length, in units, of the hypotenuse of
the triangle above?
How do I set up the problem to solve for the hypotenuse?

Answer 1

tan θ = 5 √3

opposite side = 15√3

First, calculate the angle:

tan θ = 5 √3

θ = arc tan 5 √3

θ = 83.41°

Apply the trigonometric function:

Sin θ= opposite side / hypotenuse

Replacing:

Sin 83.41° =15√3 / x

Where x is the hypotenuse

Solve for x:

x = 15√3 / (Sin 83.41°)

x = 26.15= 6 √19

Hypotenuse = 26.15 = 6 √19