Question

A student creates a scale drawing for a triangular vegetable garden. the next step to finalize the drawing is to determine the side lengths. what is the approximate length of side LA?

Answer 1

Notice that we are studying what is called an "oblique" triangle. For this, we can use the Law of Sines in order to solve for the measure of the side LA.

Since 2 angles are given, we can find the third one via the property that tells us that the addition of all angles in a triangle should render 180 degrees:

67 degrees + 37 degrees + third angle = 180 degrees

Therefore, the third angle shoul be:

Third angle = 180 - 67 - 37 = 76 degrees.

Now we use the Law of Sines that tells us a proportion that exists between the sine of an angle and the side opposite to each:

`(a)/(\sin(A))=(b)/(\sin(B))=(c)/(\sin (C))`

We can use it in our case with the given information as:

`(8.28)/(\sin(67))=(x)/(\sin (76))`

and solve for x in the proportion by multiplying both sides of the equation by sin(76):

`x=(8.28\cdot\sin(76))/(\sin(67))\approx8.7278`

Therefore, rounding this answer to two decimals we get that :

LA is 8.73 cm

Therefore, please select answer C in your list