Skip to main content
Ch. 1 - Trigonometric Functions
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. 1 - Trigonometric FunctionsProblema 50
Capitolo 2, Problema 50

Solve each problem. Height of a Lunar Peak The lunar mountain peak Huygens has a height of 21,000 ft. The shadow of Huygens on a photograph was 2.8 mm, while the nearby mountain Bradley had a shadow of 1.8 mm on the same photograph. Calculate the height of Bradley. (Data from Webb, T., Celestial Objects for Common Telescopes, Dover Publications.)

Guida verificata passo dopo passo
1
Understand that the photograph creates a scale model where the actual heights of the mountains are proportional to the lengths of their shadows on the photograph.
Set up a proportion relating the height of Huygens to its shadow length and the height of Bradley to its shadow length: \(\frac{\text{Height of Huygens}}{\text{Shadow of Huygens}} = \frac{\text{Height of Bradley}}{\text{Shadow of Bradley}}\).
Substitute the known values into the proportion: \(\frac{21000}{2.8} = \frac{\text{Height of Bradley}}{1.8}\).
Solve the proportion for the height of Bradley by cross-multiplying: \(\text{Height of Bradley} = \frac{21000 \times 1.8}{2.8}\).
Calculate the value from the expression above to find the height of Bradley.

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:
5m

Concetti chiave

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

Similar Triangles and Proportionality

When two objects cast shadows under the same lighting conditions, their heights and shadow lengths form similar triangles. This means the ratio of an object's height to its shadow length is constant, allowing us to find unknown heights by setting up proportions.
Video consigliato:
Percorso guidato
5:35
30-60-90 Triangles

Ratio and Proportion

Ratio compares two quantities, and proportion states that two ratios are equal. In this problem, the ratio of height to shadow length for Huygens and Bradley can be set equal, enabling calculation of Bradley's height using the known values.
Video consigliato:
Percorso guidato
6:04
Introduction to Trigonometric Functions

Unit Consistency and Conversion

Ensuring consistent units is crucial when solving problems involving measurements. Here, the shadows are measured in millimeters while heights are in feet, so the ratio uses the same units for shadow lengths to maintain accuracy in calculations.
Video consigliato:
Percorso guidato
06:11
Introduction to the Unit Circle
Pratica correlata
Domanda del libro di testo

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) I , r/y

566
views
Domanda del libro di testo

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) I , y/r

549
views
Domanda del libro di testo

Perform each calculation. See Example 3. 90° ― 36° 18' 47"

522
views
Domanda del libro di testo

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.

csc θ > 0 , cot θ > 0

1096
views
Domanda del libro di testo

Perform each calculation. See Example 3. 90° ― 17° 13'

627
views
Domanda del libro di testo

Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.

tan θ < 0 , cot θ < 0

1092
views