Question

Question
1
A)
Right triangle
has side lengths
,
, and
. A second right triangle,
, has side lengths of 50, 14, and 48. Find the ratio of the side opposite
to the hypotenuseof triangle
. Use this ratio to identify the location of point
in the second right triangle.
(1 point)
ABC AB = 7 BC = 24 AC = 25
A′B′C′ ∠A
ABC A′
The ratio of the opposite side to the hypotenuse is 1.04, and point is opposite the side that has length
48.
A′
The ratio of the opposite side to the hypotenuse is 0.96, and point is opposite the side that has length
48.
A′
The ratio of the opposite side to the hypotenuse is 0.96, and point is opposite the side that has length
14.
A′
The ratio of the opposite side to the hypotenuse is 0.28, and point is opposite the side that has length
14.
A′
Question
2
A)
Use the image to answer the question
.
Determine which of the following ratios is correct.
(1 point)
= = AB
DE
BC
EF
AC
DF
= = AB
BC
AC
DF
DE
EF
= = AB
EF
BC
DF
AC
DE
= = AB
DF
BC
EF
AC
DE
Question
3
Question
4
A)
A right triangle has a hypotenuse of length 40 and an angle of 25°, with a side opposite this angle oflength 16. A second right triangle also has an angle of 25°, with a hypotenuse of length 10. Determinethe length of the side opposite the 25° angle on the second triangle.
(1 point)
The side opposite the second triangle’s 25° angle has length 4.
The side opposite the second triangle’s 25° angle has length 64.
The side opposite the second triangle’s 25° angle has length 8.
The side opposite the second triangle’s 25°angle has length 8 21.
√−−
A)
A right triangle has a hypotenuse of length 16 and an angle of 45°, with a side opposite this angle oflength
. A second right triangle also has an angle of 45° and a side opposite this angle with alength of
. Determine the length of the hypotenuse in the second triangle.
(1 point)
8 2
– √
4 2
– √
The hypotenuse of the second triangle has length . 8 2
– √
The hypotenuse of the second triangle has length 8.
The hypotenuse of the second triangle has length 4.
The hypotenuse of the second triangle has length . 4 2
– √
Question
5
A)
Right triangle
has side lengths
,
, and
. A second right triangle,
, has side lengths of 30, 24, and 18. Find the ratio of the side opposite
to the hypotenuseof triangle
. Then use this ratio to identify the location of point
in the second right triangle.
(1 point)
ABC AB = 9 BC = 12 AC = 15
A′B′C′ ∠A
ABC A′
The ratio of the opposite side to the hypotenuse is 0.8, and point A′ is opposite the side that has length 24.
The ratio of the opposite side to the hypotenuse is 0.8, and point A′ is opposite the side that has length 18.
The ratio of the opposite side to the hypotenuse is 1.25, and point is opposite the side that has length
24.
A′
The ratio of the opposite side to the hypotenuse is 0.6, and point A′ is opposite the side that has length 18.

Answer 1

Here are the answers with brief explanations:

Question 1
- AB = 7, BC = 24, AC = 25 → hypotenuse = 25, side opposite ∠A = BC = 24, so ratio = 24/25 = 0.96.
- In A′B′C′ the hypotenuse is 50, so the side opposite A′ = 0.96 × 50 = 48.
Answer: "The ratio is 0.96, and point A′ is opposite the side of length 48."

Question 2
- Correct ratio: AB/EF = BC/DF = AC/DE.

Question 4 (first part: 25°)
- Opposite/hypotenuse = 16/40 = 0.4. For the second triangle with hypotenuse 10, opposite = 0.4 × 10 = 4.
Answer: 4.

Question 4 (second part: 45°)
- For hypotenuse 16, opposite = 16·sin45° = 16·(√2/2) = 8√2. If the second triangle’s opposite side is 4√2, its hypotenuse = (4√2)/(sin45°) = (4√2)/(√2/2) = 8.
Answer: 8.

Question 5
- AB = 9, BC = 12, AC = 15 → opposite/hypotenuse for ∠A = 12/15 = 0.8.
- For A′B′C′ with hypotenuse 30, opposite = 0.8 × 30 = 24.
Answer: "The ratio is 0.8, and point A′ is opposite the side of length 24."