Question

How do you solve the right triangle given A = 28° 30' , b = 18.3?

Answer 1

`∠A= 28.5º, ∠B=61.5º, ∠C=90º`
`a≈4.2, b=18.3, c≈18.8`

Explanation:

We are given this triangle:

Since there are 60 minutes in a degree, we know that `∠A= 28.5º`

Since we know `∆ABC` is a right triangle, `∠C=90º`

Since there are 180º in all triangles, `∠A+∠B+∠C=180º`, which means that `28.5º+∠B+90º=180º`, which means that `∠B=61.5º`

Now our triangle is:

Using the law of sines (`sin(A)/a=sin(B)/b`), we can obtain the length of side a: `sin(28.5)/a=sin(61.5)/18.3`

This simplifies to `sin(61.5)×a=18.3sin(28.5)`, which simplifies to `a=(18.3sin(28.5))/sin(61.5)`, which is approximately 4.2.

Now our triangle looks like this:

From here, we can solve for side c by using the pythagorean theorem (`a^2+b^2=c^2`): `(18.3)^2+(4.2)^2=c^2`

`c=sqrt((18.3)^2+(4.2)^2)=sqrt(352.53)≈18.8`

So we end with our solved triangle that looks like this: