What is the distance between (4, 7)(4,7)left parenthesis, 4, comma, 7, right parenthesis and (2, 2)(2,2)left parenthesis, 2, com
1 answer:
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Answer:
Choice A. 3.
Step-by-step explanation:
The triangle in question is a right triangle.
- The length of the hypotenuse (the side opposite to the right angle) is given.
- The measure of one of the acute angle is also given.
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:
if
;
if
;
if
.