They’ve already written most of the information you’ll need on the figure, but it can be worth noting the
side that you are looking for: the side that shows the distance from the house to the garage.
Let the answer choices help. These choices tell you a lot more than you may think: First of all, they offer
the main indication that this will be a SOHCAHTOA problem by showing that you will need to choose
sine, cosine, or tangent. Next, they tell you that you’ll only be dealing with one angle, the 38° one. Finally,
they tell you that you won’t need to do any weird rounding with decimals because they just want the sine,
cosine, or tangent expression.
Have a close look at the sides you’re dealing with. Where are they relative to the 38° angle? The base of
the triangle is touching the 38° angle, so it’s adjacent, and the side you’re looking for is opposite the 38°
angle. It looks like we won’t be dealing with the hypotenuse at all. So which trig function deals with the
opposite and adjacent sides? Remember SOHCAHTOA. The function we’ll need is tangent. And don’t
do more work than you need to. Only (F) offers an expression featuring the tangent function, so it must be
the correct answer.
Shapes Within Shapes: What’s the Link?
ACT’s favorite way to ask hard Geometry questions is to put shapes within shapes. You know the drill:
Some shape inscribed in some other shape, or two shapes share a common side. They’ve got all kinds of
ways to ask these questions. But when you see a shape drawn within another shape, there’s usually one
question that will blow the question wide open: What’s the link between the two shapes? Let’s try a few.
1. A square inscribed in a circle
2. A triangle inscribed in a rectangle
3. A square overlapping with a circle
