Question

Help w/ Trig Questions? #1

Hi, here are just two questions. I know you like to answer them as separate but there are way too many. Please show your work and make a picture to help!

Answer 1

In the `DeltaABC` to be drawn

`AB=12m,BC=10mand angle BAC=40^@`

So length of the perpendicular `BN` drawn from `B` on `AC` will be given by

`BN=ABsinangleBAC=12xxsin40~~7.71m`

But `BC=10m`

So `BC > BN and BC < AB`

So in constructing `DeltaABC` the arc of radius `10m`drawn centering `B` will intersect at two different positions (C) giving two lengths of `AC=x` and forming of two triangles becomes possible.

Answer 2

2nd part

By the problem

In `DeltaAPB`

`PA=16.2km,PB=18.9kmandangleAPB=53^@`

So applying cosine law we can write,the distance between the ruders

`AB=sqrt(PA^2+PB^2-2PAxxPBcosangleAPB)`

`=>AB=sqrt(16.2^2+18.9^2-2xx16.2xx18.9xxcos53^@)`

`~~15.8km`