Question

The length of the longer leg of a 30 60 90 triangle is 6. The shorter leg is 4.

State the solution in Simple Root Form:
State the solution to the nearest tenth:

Answer 1

Explanation:

remember the trigonometric triangle inscribed in a circle (the norm circle with radius = 1).

for a larger system the leg lengths are sine and cosine multiplied by the radius (which is the Hypotenuse of the right-angled triangle).

the longer leg is opposite of the larger angle (60°).

the shorter leg is opposite of the smaller angle (30°).

what is the desired solution ? the length of the Hypotenuse ? or what ?

6 = sin(60)×Hypotenuse

Hypotenuse = 6/sin(60) = 6/(sqrt(3)/2) = 12/sqrt(3) =

= 6.92820323... ≈ 6.9