A 20 meter tall statue casts a shadow that is 10 meters long. Will sketches the following diagram to help find the angle of elevation from the ground to the sun. Which equation can Will use to find the value of x? **Title: Finding the Angle of Elevation Using Trigonometry****Introduction**This tutorial will help you understand how to find the angle of elevation from the ground to the sun using trigonometric principles. We will use a real-world example where a 20 meter tall statue casts a 10 meter long shadow.**Problem Statement**A 20 meter tall statue casts a shadow that is 10 meters long. Will sketches the following diagram to help find the angle of elevation from the ground to the sun. Which equation can Will use to find the value of $x$?**Diagram Explanation**There is a right triangle in the diagram with:- The height of the statue (opposite side) labeled as 20 meters.- The length of the shadow (adjacent side) labeled as 10 meters.- The right angle (90 degrees) is between the height of the statue and the shadow.- The angle of elevation $x$ is located between the ground and the hypotenuse.**Mathematical Approach**To solve for the angle of elevation $x$, we use the tangent trigonometric function. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.This can be mathematically represented as:\[\tan(x) = \frac{\text{opposite}}{\text{adjacent}}\]Substituting the given values:\[\tan(x) = \frac{20}{10}\]\[\tan(x) = 2\]**Question Options**Given these concepts, the problem provides multiple-choice options to determine the correct trigonometric equation to find $x$:- $ \tan(x) = \frac{10}{20} $- $ \tan(x) = \frac{20}{10} $- $ x = \tan \left( \frac{20}{10} \right) $- $ x = \tan \left( \frac{10}{20} \right) $**Answer**The correct option is:\[\tan(x) = \frac{20}{10}\]**Conclusion**By understanding and applying the tangent function and the relation between the sides of a right triangle, we can easily determine that the angle of elevation $x$ can be found using the equation \(\tan(x) = \frac{20}{

Draw a schematic diagram of given figure.

A 20 meter tall statue casts a shadow that is 10 meters long. Will sketches the following diagram to help find the angle of elevation from the ground to the sun. Which equation can Will use to find the value of x? Statue 20 90 10 Shadow O tan(x) =10/20 O tan(x) =20/10 O x = tan (20/10) O x = tan (10/20)

A 20 meter tall statue casts a shadow that is 10 meters long. Will sketches the following diagram to help find the angle of elevation from the ground to the sun. Which equation can Will use to find the value of x? Statue 20 90 10 Shadow O tan(x) =10/20 O tan(x) =20/10 O x = tan (20/10) O x = tan (10/20)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

See similar textbooks

Related questions

Q: In which quadrant does the given point lie? (-7,0)

Q: Two helicopters leave a heliport at the same time. The first flies 190⁢km/h in a direction of 290…

A: The distance between the two helicopters after three hours is 369 kilometersExplanation:Step 1:…

Q: 8. New Horizons is an interplanetary space probe that approached the dwarf planet Pluto in 2015. How…

A: Theorem When a tangent and a secant, two secants, or two tangents intersect outside a circle then…

Q: Due to construction traffic is being detoured from Elm Street by making a 60° right turn onto Walnut…

Q: A ferris wheel has a radius of 22 feet and completes 7 revolutions in 2 minutes. Find the linear…

A: Given,r=22 feet and w(angular velocity) =72 revolution/min = 72*0.10472…

Q: A drone craft hovers in the air directly above a straight line on the ground that is 400 feet long.…

Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

**Title: Finding the Angle of Elevation Using Trigonometry**

**Introduction**
This tutorial will help you understand how to find the angle of elevation from the ground to the sun using trigonometric principles. We will use a real-world example where a 20 meter tall statue casts a 10 meter long shadow.

**Problem Statement**
A 20 meter tall statue casts a shadow that is 10 meters long. Will sketches the following diagram to help find the angle of elevation from the ground to the sun. Which equation can Will use to find the value of $x$?

**Diagram Explanation**
There is a right triangle in the diagram with:
- The height of the statue (opposite side) labeled as 20 meters.
- The length of the shadow (adjacent side) labeled as 10 meters.
- The right angle (90 degrees) is between the height of the statue and the shadow.
- The angle of elevation $x$ is located between the ground and the hypotenuse.

**Mathematical Approach**
To solve for the angle of elevation $x$, we use the tangent trigonometric function. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

This can be mathematically represented as:
\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}}
\]

Substituting the given values:
\[
\tan(x) = \frac{20}{10}
\]
\[
\tan(x) = 2
\]

**Question Options**
Given these concepts, the problem provides multiple-choice options to determine the correct trigonometric equation to find $x$:

- $ \tan(x) = \frac{10}{20} $
- $ \tan(x) = \frac{20}{10} $
- $ x = \tan \left( \frac{20}{10} \right) $
- $ x = \tan \left( \frac{10}{20} \right) $

**Answer**
The correct option is:
\[
\tan(x) = \frac{20}{10}
\]

**Conclusion**
By understanding and applying the tangent function and the relation between the sides of a right triangle, we can easily determine that the angle of elevation $x$ can be found using the equation \(\tan(x) = \frac{20}{

Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Ratios$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

Please answer with a neat presentation, so that it's easy to read. Also, if you could show your work so that I can see what you did. Thank you.
The height of a pole is 23.66m. If the angle of elevation changes from 60 to 45 then the Length of the shadow will increase by how many meters?
The Eiffel tower is 970 feet talle If the shadow iS 1200 feet lang at 11:00 am, what is the angle of elevation to the top Of the tower qt the time of day.
stacie is driving 60 mph in a car whose wheels have a 30 inch diameter. find the angular speed of the wheels
Please give me answers in 5min I will give you like sure
You are flying a drone to get a nice picture of a lighthouse. As your drone is hovering above the ground, the angle of depression to the base of the lighthouse is 60 degrees, and the angle of elevation to the top of the lighthouse is 45 degrees. Your drone determines that it is exactly 120 feet from the base of the lighthouse. Using this information, determine the height of the lighthouse in feet
You are standing 100 meters from the base of a tower. The angle of elevation from where you are standing to the top of the tower is 38 degrees. How tall is the tower?
Picture
A person stands on the top of a 165165 foot tall cliff looking at a boat out on the water. The angle of depression from the cliff to the boat is 33 degrees. Find the distance from the boat to the base of the cliff. Round your answer to 3 decimal places.