1 Answer

Ask a Question

Ashar · Answer 1 · 2023-03-15T04:00:22+0000

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:

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:

$\begin{gathered} \cos B=\frac{200.7\operatorname{km}}{401.5\operatorname{km}}=(2007)/(4015)\text{.} \\ \sin A=\frac{200.7\operatorname{km}}{401.5\operatorname{km}}=(2007)/(4015)\text{.} \end{gathered}$

Therefore:

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

Answer:

$\begin{gathered} b=347.74\operatorname{km}, \\ B=60.00^(\circ), \\ A=30.00^(\circ) \end{gathered}$

0 Comments

Your comment on this question:

Your answer

1 Answer

0 Comments

Your comment on this answer:

Other Questions