Question
Question 1
A)A building casts a shadow reaching 13 feet from the base of the building, with a diagonal distance of 15 feet from the top of the building. Using the inverse of sine, what is the approximate angle formed between the top of the building and the shadow?(1 point)
Responses
90°
90°
30°
30°
45°
45°
60°
60°
Question 2
A)Jessica sets up a volleyball net in her backyard. To secure the net in place, she extends a rope from the top of each of the two poles at a diagonal to the ground. Once the poles are placed in the ground, they are 7 feet tall; the rope she uses is 9 feet long. Using the inverse of sine, what is the approximate angle formed between the ground and the rope?(1 point)
Responses
39°
39°
45°
45°
51°
51°
90°
90°
Question 3
A)You are to construct a decorative wood shelf that has two metal angle supports that fasten to the bottom of the shelf and resemble a right triangle. The shelves are to stick out from the wall 1 foot, and the diagonal distance of the metal piece is 1.25 feet. Using the inverse of sine, what is the approximate angle formed where the metal piece rests on the wall?(1 point)
Responses
90°
90°
37°
37°
53°
53°
61°
61°
Question 4
A)Romeo owns a business that puts up and takes down holiday lights. He is working on a house and places the base of his 20-foot ladder at a 4-foot distance from the house. Using the inverse of sine, what is the approximate angle formed where the ladder rests on the house?(1 point)
Responses
12°
12°
78°
78°
34°
34°
90°
90°
Question 5
A)A 15-foot ladder is leaning against a tree. The base of the ladder is 8 feet away from the tree base. Using the inverse of sine, what is the approximate angle between the ladder and the tree? (1 point)
Responses
32°
32°
90°
90°
25°
A)A building casts a shadow reaching 13 feet from the base of the building, with a diagonal distance of 15 feet from the top of the building. Using the inverse of sine, what is the approximate angle formed between the top of the building and the shadow?(1 point)
Responses
90°
90°
30°
30°
45°
45°
60°
60°
Question 2
A)Jessica sets up a volleyball net in her backyard. To secure the net in place, she extends a rope from the top of each of the two poles at a diagonal to the ground. Once the poles are placed in the ground, they are 7 feet tall; the rope she uses is 9 feet long. Using the inverse of sine, what is the approximate angle formed between the ground and the rope?(1 point)
Responses
39°
39°
45°
45°
51°
51°
90°
90°
Question 3
A)You are to construct a decorative wood shelf that has two metal angle supports that fasten to the bottom of the shelf and resemble a right triangle. The shelves are to stick out from the wall 1 foot, and the diagonal distance of the metal piece is 1.25 feet. Using the inverse of sine, what is the approximate angle formed where the metal piece rests on the wall?(1 point)
Responses
90°
90°
37°
37°
53°
53°
61°
61°
Question 4
A)Romeo owns a business that puts up and takes down holiday lights. He is working on a house and places the base of his 20-foot ladder at a 4-foot distance from the house. Using the inverse of sine, what is the approximate angle formed where the ladder rests on the house?(1 point)
Responses
12°
12°
78°
78°
34°
34°
90°
90°
Question 5
A)A 15-foot ladder is leaning against a tree. The base of the ladder is 8 feet away from the tree base. Using the inverse of sine, what is the approximate angle between the ladder and the tree? (1 point)
Responses
32°
32°
90°
90°
25°
Answers
Answered by
GPT-4o mini
To solve these questions, we will use the inverse sine function, which is given by the formula:
\[
\text{Angle} = \arcsin\left(\frac{\text{Opposite}}{\text{Hypotenuse}}\right)
\]
Where:
- "Opposite" is the length of the side opposite the angle we are trying to find.
- "Hypotenuse" is the diagonal distance (or the length of the ladder, rope, etc.).
**Question 1:**
- Opposite = height of the building (unknown)
- Adjacent = shadow length = 13 feet
- Hypotenuse = diagonal distance = 15 feet
Using the Pythagorean theorem:
\[
\text{height}^2 + 13^2 = 15^2 \\
\text{height}^2 + 169 = 225 \\
\text{height}^2 = 56 \\
\text{height} \approx 7.48 \text{ feet}
\]
Now we can find the angle:
\[
\text{Angle} = \arcsin\left(\frac{\text{height}}{15}\right) = \arcsin\left(\frac{7.48}{15}\right) \\
\approx \arcsin(0.4987) \approx 29.9° \approx 30°
\]
**Correct Answer: 30°**
---
**Question 2:**
- Opposite = height of the pole = 7 feet
- Hypotenuse (rope length) = 9 feet
Using the inverse sine:
\[
\text{Angle} = \arcsin\left(\frac{7}{9}\right) \\
\approx \arcsin(0.7778) \approx 51.0°
\]
**Correct Answer: 51°**
---
**Question 3:**
- Opposite = 1 foot (the distance the shelf sticks out)
- Hypotenuse = 1.25 feet (length of the metal piece)
Calculating the angle:
\[
\text{Angle} = \arcsin\left(\frac{1}{1.25}\right) \\
= \arcsin(0.8) \approx 53.1° \approx 53°
\]
**Correct Answer: 53°**
---
**Question 4:**
- Opposite = height of the ladder at the point touching the house (unknown)
- Adjacent = distance from the house = 4 feet
- Hypotenuse = length of the ladder = 20 feet
First, find the height:
\[
\text{height}^2 + 4^2 = 20^2 \\
\text{height}^2 + 16 = 400 \\
\text{height}^2 = 384 \\
\text{height} \approx 19.6 \text{ feet}
\]
Calculating the angle:
\[
\text{Angle} = \arcsin\left(\frac{19.6}{20}\right) \\
= \arcsin(0.98) \approx 78.5° \approx 78°
\]
**Correct Answer: 78°**
---
**Question 5:**
- Opposite = height (unknown, let's calculate it using Pythagorean theorem)
- Adjacent = distance from the tree = 8 feet
- Hypotenuse = length of the ladder = 15 feet
Finding the height:
\[
\text{height}^2 + 8^2 = 15^2 \\
\text{height}^2 + 64 = 225 \\
\text{height}^2 = 161 \\
\text{height} \approx 12.688 \text{ feet}
\]
Calculating the angle:
\[
\text{Angle} = \arcsin\left(\frac{12.688}{15}\right) \\
= \arcsin(0.8459) \approx 57.8° \approx 25°
\]
None of the suggested options fit this answer; if your possible responses include other angles, please verify.
Hope this helps! Would you like further assistance?
\[
\text{Angle} = \arcsin\left(\frac{\text{Opposite}}{\text{Hypotenuse}}\right)
\]
Where:
- "Opposite" is the length of the side opposite the angle we are trying to find.
- "Hypotenuse" is the diagonal distance (or the length of the ladder, rope, etc.).
**Question 1:**
- Opposite = height of the building (unknown)
- Adjacent = shadow length = 13 feet
- Hypotenuse = diagonal distance = 15 feet
Using the Pythagorean theorem:
\[
\text{height}^2 + 13^2 = 15^2 \\
\text{height}^2 + 169 = 225 \\
\text{height}^2 = 56 \\
\text{height} \approx 7.48 \text{ feet}
\]
Now we can find the angle:
\[
\text{Angle} = \arcsin\left(\frac{\text{height}}{15}\right) = \arcsin\left(\frac{7.48}{15}\right) \\
\approx \arcsin(0.4987) \approx 29.9° \approx 30°
\]
**Correct Answer: 30°**
---
**Question 2:**
- Opposite = height of the pole = 7 feet
- Hypotenuse (rope length) = 9 feet
Using the inverse sine:
\[
\text{Angle} = \arcsin\left(\frac{7}{9}\right) \\
\approx \arcsin(0.7778) \approx 51.0°
\]
**Correct Answer: 51°**
---
**Question 3:**
- Opposite = 1 foot (the distance the shelf sticks out)
- Hypotenuse = 1.25 feet (length of the metal piece)
Calculating the angle:
\[
\text{Angle} = \arcsin\left(\frac{1}{1.25}\right) \\
= \arcsin(0.8) \approx 53.1° \approx 53°
\]
**Correct Answer: 53°**
---
**Question 4:**
- Opposite = height of the ladder at the point touching the house (unknown)
- Adjacent = distance from the house = 4 feet
- Hypotenuse = length of the ladder = 20 feet
First, find the height:
\[
\text{height}^2 + 4^2 = 20^2 \\
\text{height}^2 + 16 = 400 \\
\text{height}^2 = 384 \\
\text{height} \approx 19.6 \text{ feet}
\]
Calculating the angle:
\[
\text{Angle} = \arcsin\left(\frac{19.6}{20}\right) \\
= \arcsin(0.98) \approx 78.5° \approx 78°
\]
**Correct Answer: 78°**
---
**Question 5:**
- Opposite = height (unknown, let's calculate it using Pythagorean theorem)
- Adjacent = distance from the tree = 8 feet
- Hypotenuse = length of the ladder = 15 feet
Finding the height:
\[
\text{height}^2 + 8^2 = 15^2 \\
\text{height}^2 + 64 = 225 \\
\text{height}^2 = 161 \\
\text{height} \approx 12.688 \text{ feet}
\]
Calculating the angle:
\[
\text{Angle} = \arcsin\left(\frac{12.688}{15}\right) \\
= \arcsin(0.8459) \approx 57.8° \approx 25°
\]
None of the suggested options fit this answer; if your possible responses include other angles, please verify.
Hope this helps! Would you like further assistance?
There are no human answers yet. A form for humans to post answers is coming very soon!