Question

Two markers A and B on the same side of a canyon rim are 56 feet apart. A third marker C, located across the rim. is positioned so that BAC = 69º and ABC = 51° Complete parts (a) and (b) below (a) Find the distance between C and A.

Answer 1

To answer this question, it will be helpful to have a drawing of the situation to find the asked distance:

With this information, it will be easier to have all the information to solve for the distance CA.

Therefore, to find the distance CA, we can apply the Law of Sines, in which we have to find the angle C. We know that the sum of the interior angles of a triangle is equal to 180. Then, we have:

`mNow, we can apply the Law of Sines to find the distance CA:[tex](AC)/(\sin(51))=(56)/(\sin(60))\Rightarrow AC=(56\cdot\sin (51))/(\sin (60))`

Then, we have:

`AC=50.2527681652ft`

Then, to round to one decimal place, we have that AC is approximately 50.3 ft.

To find the distance between the two rims, we have:

Now, we can also apply the Law of Sines to find the distance CD (the distance between the two rims):

`(CD)/(\sin(69))=(CA)/(\sin(90))\Rightarrow CD=CA\cdot\sin (69),\sin (90)=1`

Then, we have:

`CD=50.2527681652\cdot\sin (69)\Rightarrow CD=46.9150007363ft`

Therefore, the distance between the two canyon rims (round to one decimal place) is 46.9 ft.

If we take 50.3 ft (for CA), instead, we have 47 ft.