Skip to main content
Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblema 55
Capitolo 3, Problema 55

Solve each problem. See Examples 3 and 4. Angle of Depression of a Light A company safety committee has recommended that a floodlight be mounted in a parking lot so as to illuminate the employee exit, as shown in the figure. Find the angle of depression of the light to the nearest minute.

Guida verificata passo dopo passo
1
Identify the right triangle formed by the floodlight, the point on the ground where the light is aimed (employee exit), and the vertical height of the floodlight from the ground.
Label the height of the floodlight as the opposite side and the horizontal distance from the base of the floodlight to the employee exit as the adjacent side of the right triangle.
Recall that the angle of depression from the floodlight to the employee exit corresponds to the angle between the horizontal line from the floodlight and the line of sight to the exit, which is congruent to the angle inside the triangle adjacent to the horizontal side.
Use the tangent trigonometric ratio, which relates the opposite side and adjacent side: \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\) where \(\theta\) is the angle of depression.
Calculate \(\theta\) by taking the inverse tangent (arctangent) of the ratio: \(\theta = \tan^{-1}\left(\frac{\text{opposite}}{\text{adjacent}}\right)\), then convert the decimal degrees to degrees and minutes to express the angle to the nearest minute.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Angle of Depression

The angle of depression is the angle formed between the horizontal line from the observer's eye and the line of sight looking downward to an object. It is measured downward from the horizontal and is congruent to the angle of elevation from the object to the observer.
Video consigliato:
Percorso guidato
04:46
Coterminal Angles

Right Triangle Trigonometry

Right triangle trigonometry involves using sine, cosine, and tangent ratios to relate the angles and sides of a right triangle. These ratios help find unknown lengths or angles when some measurements are given, which is essential in solving problems involving angles of elevation or depression.
Video consigliato:
Percorso guidato
04:39
45-45-90 Triangles

Converting Decimal Degrees to Degrees and Minutes

Angles are often expressed in degrees, minutes, and seconds, where one degree equals 60 minutes. Converting decimal degrees to degrees and minutes involves separating the integer part as degrees and multiplying the decimal part by 60 to find the minutes, providing a more precise angle measurement.
Video consigliato:
Percorso guidato
5:04
Converting between Degrees & Radians
Pratica correlata
Domanda del libro di testo

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Length of Sides of an Isosceles Triangle An isosceles triangle has a base of length 49.28 m. The angle opposite the base is 58.746°. Find the length of each of the two equal sides.

747
views
Domanda del libro di testo

Solve each problem.See Examples 3 and 4. Angle of Elevation of the Sun The length of the shadow of a building 34.09 m tall is 37.62 m. Find the angle of elevation of the sun to the nearest hundredth of a degree.

756
views
Domanda del libro di testo

Solve each problem. See Examples 3 and 4. Length of a Shadow Suppose that the angle of elevation of the sun is 23.4°. Find the length of the shadow cast by a person who is 5.75 ft tall.

<Image>

684
views
Domanda del libro di testo

Determine whether each statement is true or false. If false, tell why. See Example 4. cos(30° + 60°) = cos 30° + cos 60°

657
views
Domanda del libro di testo

Determine whether each statement is true or false. If false, tell why. See Example 4. cos 60° = 2 cos² 30° - 1

739
views
Domanda del libro di testo

Give the exact value of each expression. See Example 5. sec 45°

620
views