Find the longer leg of the triangle.
a. 3
b.
c. 9
d.

Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let denotes the length of the side opposite to the acute angle, and be the length of the side next to this acute angle.

.

Similarly,

.

The longer leg in this case is the one adjacent to the acute angle. The answer will be .

There's a shortcut to the answer. Notice that . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the angle will be the longer leg. There will be no need to find the length of the opposite leg.

Does this relationship holds for all acute angles? (That is, ?) It turns out that:

A

Step-by-step explanation:

Since the triangle is right use the cosine ratio

cos30° = = , so

=

Multiply both sides by 2

adj = × 2 = 3

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