How do you solve this problem?

[Yizewu]

I've been trying this problem for ages but I can't seem to know how to find the area of the industrial zone. Only one angle is given, the 90 degree triangle and one side of it is 1.4km. How do you use trig to find the sides and then the area of the zone?

 

[R.M.]

If King Street & Queen Street are parallel, what conclusion can you make about the triangles? What is the area of the smaller triangle? See if those two answers can be put together to find the Industrial zone area.

 

[Mr. Bland]

If King and Queen are indeed parallel, then the criss-crossing Main and Railway form two triangles that are proportional to one another. If the 1.0 km length and the 3.0 km lengths are proportional, then the 1.4 km length will scale to the industrial zone as well.

 

[Steven G]

3/1 = 3, so multiply 1.4 by 3. Then what?
Sorry for giving such a big hint but if the OP did not see this after spending ages on it then maybe the op will never see it.

 

[Otis]

I note that Yizewu has marked the thread as 'solved'. (I'm not sure whether the exercise instructed use of trigonometry, to find triangle measurements.)

For readers using the area formula, we need only the height (h) of the shaded triangle. We know the base (b) is 3.

Area = 1/2 · b · h

We know the two triangles are similar because their corresponding angles are all equal.

Therefore, corresponding sides are all proportional. We can say, "h compares to 3 in the same way as 1.4 compares to 1". We can write and solve that proportion for h.

?