**Problem Statement:**2. The shadow of a building is cast by the sun at an angle of 60° above the horizon. Later, the shadow is now 10 meters longer, and the sun is at an angle of 30° above the horizon.**Instruction:**A. Draw a diagram that models this scenario.**Explanation of Diagram:**1. **Initial Condition:** - **Building:** Represent the building as a vertical line of unknown height \( H \). - **Sun's Angle (60°):** Draw a horizontal line from the base of the building and a line tilted at a 60° angle above this horizontal line, representing the direction of the sunlight. - **Shadow:** Mark the point where this sunlight meets the ground. The horizontal distance from the base of the building to this point is the shadow length \( S \).2. **Later Condition:** - **Sun's Angle (30°):** Draw another horizontal line from the base of the building and another line tilted at a 30° angle above this horizontal line, representing the new direction of the sunlight. - **Extended Shadow:** Extend the shadow by 10 meters beyond the initial shadow length \( S \). Represent this total length as \( S + 10 \).3. **Geometric Relationships:** - Use trigonometric functions to relate the height of the building and the lengths of shadows. - For the initial shadow: \[ S = H \cdot \cot(60°) \] - For the later, longer shadow: \[ S + 10 = H \cdot \cot(30°) \]**Objective:** - Using the given angles and the increase in shadow length, compute the height of the building \( H \) and the lengths of the shadows \( S \) and \( S + 10 \) using trigonometric relationships.

Lets say initial length of the shadow was 'x' meter and height of the building is 'h' meter.

2. The shadow of a building is cast by the sun at an angle of 60° above the horizon. Later, the shadow is now 10 meters longer, and the sun is at an angle of 30° above the horizon. A. Draw a diagram that models this scenario

2. The shadow of a building is cast by the sun at an angle of 60° above the horizon. Later, the shadow is now 10 meters longer, and the sun is at an angle of 30° above the horizon. A. Draw a diagram that models this scenario

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: 4. A student wants to measure the height of a rock pillar in a river. The student stands at point C…

Q: 7. Choose the correct answer. Two angles commonly used in surveying are the angle of elevations and…

A: Angles of elevation and depression are angles that are formed with respect to the horizontal. If the…

Q: 4 b. Parallelogram MNOP is rotated 180° about the origin and then reflected across the y-axis. What…

Q: The famous Regiomontanus’ problem for angle maximization was proposed during the 15th century. A…

Q: 4. *The Leaning Tower of Pisa is inclined 5.5° from the vertical. At a distance of 100 meters from…

A: Question No. (4):The Leaning Tower of Pisa is inclined from the vertical. At a distance of 100…

Q: Please provide detailed solution easily understandable.

A: Step 1 : We have a right tringle with perpendicular sides 1, 12 . Slope =1/12 .By the tangent ratio…

Q: Air Traffic Control at a local airport keeps track of various aircraft on a radar screen that has…

Q: You're helping plan the construction of a rope bridge across a bottomless trench. You chose two…

A: a. Given:Angle between stake A and planned location of the bridge: 85°Angle between stake B and…

Q: 4. If ABCD is a parallelogram, find mZD. B А. 6° В. 53° С. 127° (9x – 1)° (13х - 25)° A D D. 141°

A: Opposite angles of a parallelogram are equal. And adjacent angles measure 180 when added.

Q: If (x, y) is a point on the unit circle in quadrant IV and if V3 what is y? (p. 35)

A: Given : if (x , y ) is a point on the unit circle in the quadrant IV and if x=32. then we have to…

Q: 22. For a ladder to be safe, the angle of elevation of the ladder must be between 70° and 78°. An 18…

A: Given that for a ladder to be safe, the angle of elevation of the ladder must be between 70° and…

Q: An ant looks up at a UFO at an angle of elevation of 23 degrees. The ant noticed that the shadow of…

Q: 5: A party planner is trying to hang a sign between a house and a palm tree for someone's birthday…

A: Given: A party planner is trying to hang a sign between a house and a palm tree for someone's…

Q: 2. A 6-m ladder is leaning against a wall so that the ladder's angle of inclination is 75°. Which…

Q: Find the value of x for which line a is parallel to line b.

A: It is given that, line a and b are parallel lines,

Q: You are visiting Las Vegas, NV. From the “strip”, you can see mountains, and a quick measurement…

Q: 9. A man in a row boat at point P, 5 miles from the nearest point A on a straight shore, wishes to…

Q: b) You are fishing on a dock which is 5 feet above the water. You catch a fish! And you reel it in…

Question

**Problem Statement:**
2. The shadow of a building is cast by the sun at an angle of 60° above the horizon. Later, the shadow is now 10 meters longer, and the sun is at an angle of 30° above the horizon.

**Instruction:**
A. Draw a diagram that models this scenario.

**Explanation of Diagram:**
1. **Initial Condition:**
- **Building:** Represent the building as a vertical line of unknown height \( H \).
- **Sun's Angle (60°):** Draw a horizontal line from the base of the building and a line tilted at a 60° angle above this horizontal line, representing the direction of the sunlight.
- **Shadow:** Mark the point where this sunlight meets the ground. The horizontal distance from the base of the building to this point is the shadow length \( S \).

2. **Later Condition:**
- **Sun's Angle (30°):** Draw another horizontal line from the base of the building and another line tilted at a 30° angle above this horizontal line, representing the new direction of the sunlight.
- **Extended Shadow:** Extend the shadow by 10 meters beyond the initial shadow length \( S \). Represent this total length as \( S + 10 \).

3. **Geometric Relationships:**
- Use trigonometric functions to relate the height of the building and the lengths of shadows.
- For the initial shadow:
\[ S = H \cdot \cot(60°) \]
- For the later, longer shadow:
\[ S + 10 = H \cdot \cot(30°) \]

**Objective:**
- Using the given angles and the increase in shadow length, compute the height of the building \( H \) and the lengths of the shadows \( S \) and \( S + 10 \) using trigonometric relationships.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

2. A golfer hit her tee shot so that it landed about 21 ft behind a 40-ft tall pine tree. She decided to take her second shot and hoped it would make it over the top of the tree. She used her lob wedge and hit the ball, sending it upward at an angle of 60°. Was she able to clear the top of the tree? Show calculations to support your conclusion. a. b. Draw and label a picture of the information presented in this question. Determine if the golfer was able to clear the top of the tree. Show calculations to support your conclusion.
2:06 AM Mon Jun 27 MTH1W Culminat...ty - V6 copy copy Question 8 Home Insert 5.2 m Select Objects Draw 0.8m Layout Review View Question 7 Conveyor belts are being set up in the factory to assist with the manufacturing. [Hint: Lesson 9.3] The length of one of the conveyor belts was 5.2 m. It needs to be set up as shown below. What horizontal distance is needed on the floor to set up the conveyor belt? Round your answer to two places of decimal. ода Draw with Touch 16
Refer to figure below and answer the following questions. 1. What are the points that lie on the circle? 2. What could be the coordinates of the other points on the circle? 3. What is the equation of the circle in the figure below? Fig 5.6
Three Concrete Slabs. Suppose there are three concrete rectangular slabs standing or resting on level ground in the order that is depicted in the diagram below. The angle of depression from Slab 2 to Slab 1 is 22°and they are 8 feet apart. Slab 3 is leaning on Slab 2 making an angle of 40° with a vertical reference line. Find the height of Slab 2 and the length of Slab 3. 40° Slab 3 Slab 2 22 Slab1 2ft -Level Ground 8ft
04 PM Thu Mar 25 10. Given: APQR is an isosceles triangle with vertex angle Q PQ = 5x - 24, QR = 3x –2, and PR = 5x - 8. Find the information that can be used to complete the sentence below. The length of each leg of APQR is and the length of the base is
Determine whether the following situations illustrate an angle of elevation or an angle of depression by writing LOOK UP or LOOK DOWN on the blank provided before the number. 1. gazing at the stars at night 2. watching the passers-by and the vehicles in the street from a rooftop 3. making eye contact with the audience while delivering a speech from the stage 4. seeing an airplane traveling through the sky 5. taking a selfie with your phone slightly upward 6. scrolling through your Facebook feed while sitting 7. seeing a bird's nest up a tree 8. looking at your own shadow 9. reaching for an object at a higher layer of a shelf with your hands 10. picking up something you dropped