+0

+2
527
3
+459

May 22, 2017
edited by ZZZZZZ  May 22, 2017

#1
+7348
+2

Here I made a triangle where A is the first sighting, B is the light, and C is the second sighting.

The question is, what is the length of BC ?

On this first one, I just focused on the angles.

m∠BAC = 107º - 60º   =   47º

measure of the green angle = 180º - 107º   =   73º

Since the two vertical lines are parallel and line AC crosses them, we have two parallel lines cut by a transversal. So.. the two green angles are the same.

Now let's just look at the second triangle.

We can use law of sines to find BC.

$$\frac{1.5}{\sin 26}=\frac{BC}{\sin 47} \\~\\ \frac{1.5}{\sin 26}*\sin 47 =BC \\~\\ 2.503\text{ km} \approx BC$$

.
May 23, 2017

#1
+7348
+2

Here I made a triangle where A is the first sighting, B is the light, and C is the second sighting.

The question is, what is the length of BC ?

On this first one, I just focused on the angles.

m∠BAC = 107º - 60º   =   47º

measure of the green angle = 180º - 107º   =   73º

Since the two vertical lines are parallel and line AC crosses them, we have two parallel lines cut by a transversal. So.. the two green angles are the same.

Now let's just look at the second triangle.

We can use law of sines to find BC.

$$\frac{1.5}{\sin 26}=\frac{BC}{\sin 47} \\~\\ \frac{1.5}{\sin 26}*\sin 47 =BC \\~\\ 2.503\text{ km} \approx BC$$

hectictar May 23, 2017
#2
+95884
+2

Very nice, hectictar.......!!!

May 23, 2017
#3
+459
+1

thanks hectictar

May 30, 2017