Question

Solve right triangle ABC for all missing parts. Express angles in decimal degrees.a = 200.7 km, c= 401.5 kmRound to the nearest hundred

Answer 1

Using the Pythagorean Theorem we get:

`c^2=a^2+b^2\text{.}`

Therefore:

`b^2=c^2-a^2\text{.}`

Substituting a=200.7km and c=401.5km we get:

`b^2=(401.5km)^2-(200.7km)^2.`

Solving the above equation for b we get:

`\begin{gathered} b=\sqrt[]{(401.5km)^2-(200.7km)^2} \\ =\sqrt[]{161202.25km^2-40280.79km^2} \\ =\sqrt[]{120921.76km^2}\approx347.74km\text{.} \end{gathered}`

Now, from the given diagram we get that:

`\begin{gathered} \cos B=(a)/(c), \\ \sin A=(a)/(c)\text{.} \end{gathered}`

Substituting a=200.7km and c=401.5km we get:

Therefore:

`\begin{gathered} B=\cos ^(-1)((2007)/(4015))\approx60.00^(\circ), \\ A=\sin ^(-1)((2007)/(4015))\approx30.00^(\circ), \end{gathered}`

Answer: