A particular right triangle has an acute angle of π/6 radians, and the side opposite this angle has measure 8. What is the hypotenuse of this triangle?

Answer 1

In this problem a right triangle is given, which means that the three angles are 30, 60 and 90 degrees or ∏/6, ∏/3 and ∏/2.

1. Drawing a triangle with the opposite side of Π/6 = 8 , I am going to use the definition of sine = opposite side / hypotenuse to find the hypotenuse.
2. sin (Π/6) = opp/ hyp = 8 /(x)

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8

3. . Cross multiplying, I got x=. (8) /( sin Π/6)=. 8/(1/2). = 16 sin(Π/6)= sin 30º= 1/2

The answer is that the hypotenuse is 16.

To verify the findings,

I found the missing side by using Pythagorean theorem C^2 = a^2 +b^2

16^2 = 8^2 +b^2 256= 64 + b^2 b^2 = 192. b≈13.8564

Now I found the sin (Π/3) =. 13.856 /16 ≈ 0.86602, which prove that the values found was good.

sin 60=cos 30≅0.866

Answer 2

The sine of an angle is the opposite / hypotenuse. (sin = O/H)

Write the equation:

sin (π/6) = 8 / H

rearrange:

H = 8 / sin (π/6)

Plug this into your calculator. Remember that this angle is in radians