finding width of river

[nickname]

I need help with the following problem:

angela wishes to find the distance from point A to her friend Carmen's house at point C on the other side of the river. She knows the distance from A to Betty's house at B is 540feet. The measurement of angles A and B are 57degrees and 46, respectively. Calculate distane from A to C.

I did:

Angle C= 180-(57+46)= 77degrees

(sinC/AB)=(sinB/AC)--------> AC=(ABsinB/sinC)=(540sin46/sin77)= 398ft, which is the correct answer (is this the correct way of solving this problem?)

Then I have to find the width of the river, assuming that the houses are on the very straight banks of the river? How do I solve this part?

I did (398sin57)/(sin77)= 342.6ft, but the correct answer is 334ft.


Thank you for your help!

 

[Denis]

Then I have to find the width of the river, assuming that the houses are on the very straight banks of the river?
How do I solve this part?
I did (398sin57)/(sin77)= 342.6ft, but the correct answer is 334ft.

Draw the darn triangle; then draw height line from C to AB; use right triangle.

 

[mmm4444bot]

DUPLICATE POST

 

[TchrWill]

Then I have to find the width of the river, assuming that the houses are on the very straight banks of the river? How do I solve this part?

I did (398sin57)/(sin77)= 342.6ft, but the correct answer is 334ft.

You were almost there.

398.66/sin90 = w/sin57 making w = 398.66(sin57) = 334.3.