Answer:
Step-by-step explanation:
You only need to have a general knowledge of right triangles to choose the correct answer here.
x is the long side of the right triangle. As such, it will be longer than the short side, so cannot be less than about 0.7×18 = 12.6. It cannot be longer than the hypotenuse, so must be less than 18.
Just from our knowledge of right triangle relations, we already know ...
12.6 < x < 18
There is only one answer choice in that range: 16.9.
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The unknown side is the side opposite the given angle. The other given side is the hypotenuse. The trig relation between the three given values is ...
Sin = Opposite/Hypotenuse
Multiplying by the hypotenuse, we have ...
Opposite = Hypotenuse × Sin
x = 18·sin(70°) ≈ 16.9145
x ≈ 16.9
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<em>Additional comments</em>
The mnemonic SOH CAH TOA is usually offered to help you remember the relation used above: SOH ⇒ Sin = Opposite/Hypotenuse
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You may recall that an isosceles right triangle has sides in the ratio 1:1:√2. (This is handy to remember.) That is, the shortest that the long side of a right triangle will ever be is 1/√2 ≈ 0.7071 times the length of the hypotenuse. (It is often sufficient to remember this is more than 1/2 of the hypotenuse.) Of course, it will always be shorter than the hypotenuse, and always longer than the short side.
In this triangle, you know x is the long side because it is opposite the larger of the acute angles. (The relative lengths on the drawing cannot always be trusted.)
