Right triangle ABC
has side lengths AB=6
, BC=8
, and CA=10
. A second right triangle has corresponding vertices of A′
, B′
, and C′
, with side lengths of 32, 40, and 24. In 3–5 sentences, describe how to find the ratio of the side opposite ∠A
to the hypotenuse of triangle ABC
. Then use this ratio to identify the location of point A′
in the second right triangle.(4 points)
Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is very clear.
The answer is fully supported by details.
There may be a few errors in grammar, usage, or mechanics. Errors do not interfere with meaning.
3
The answer is mostly clear.
The answer is supported by mostly relevant details.
There are a few errors in grammar, usage, or mechanics. Errors do not interfere with meaning.
2
The answer is somewhat clear.
Details are weak or not related.
There are some errors in grammar, usage, and mechanics. Errors interfere with meaning.
1
The answer is not clear.
There are few or no supporting details.
There are many errors in grammar, usage, and mechanics. Errors interfere with meaning.
0 The question is not answered.
To find the ratio of the side opposite angle A to the hypotenuse in triangle ABC, we can use the trigonometric function sine. The sine of angle A is equal to the side opposite angle A (BC) divided by the hypotenuse (CA). In this case, sin(A) = BC / CA = 8 / 10 = 4 / 5.
Using this ratio, we can identify the location of point A' in the second right triangle. Since the side opposite angle A in the second triangle is 32 (4 times the length of BC in triangle ABC) and the hypotenuse is 40 (4 times the length of CA in triangle ABC), the ratio of the side opposite angle A in triangle A'B'C' to the hypotenuse is also 4 / 5. Therefore, point A' in the second right triangle is located opposite an angle whose sine is 4 / 5.