Home > Trigonometry > The Law of Sines

How do you solve the triangle when α = 30.0°, a = 4.53, b = 9.06?

Answer 1

Madelyn Adams

Please see below.

The law of sines gives us:

#a/sinalpha=b/sinbeta#

#asinbeta=bsinalpha#

#sinbeta=(bsinalpha)/a=((9.06)(sin30^@))/4.53=((9.06)(0.5))/4.53=4.53/4.53=1#

#beta=arcsin(1)=90^@#

#gamma=180^@-(30^@+90^@)=180^@-120^@=60^@#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Zoe Austin

Read below.

I will try to solve all of the triangle's sides and angles using the Laws of Sines.

Laws of Sines states that #Sin(alpha)/a=Sin(beta)/b=Sin(gamma)/c#

We are assuming that the variables were labeled like the following:
Since we know the shortest and the longest side, we see that the missing side is the side opposite to #60#degrees.

We now simply multiply our shortest side by #sqrt3#.
#c=4.53sqrt3#
#c~~7.846#
Our triangle now will look like this:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.