1. On a sunny day, a \( 50 \mathrm{ft} \) flagpole casts a shadow that changes with the angle of elevation of the Sun. Let ' \( s \) ' be the length of the shadow and ' \( \theta \) ' the angle of elevation of the Sun. Find the rate at which the length of the shadow is changing with respect to \( \theta \) when \( \theta=45^{\circ} \). Express your answer in units of feet/degree.
Added by David T.
Close
Step 1
From the diagram, we can see that the flagpole height (50 ft) and shadow length (s) form a right triangle with the sun's rays. Using tangent: tan(θ) = 50/s Therefore: s = 50/tan(θ) Show more…
Show all steps
Your feedback will help us improve your experience
Gwen Stroup and 89 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A 50-ft pole casts a shadow as shown in the figure. (a) Express the angle of elevation $\theta$ of the sun as a function of the length $s$ of the shadow. (b) Find the angle $\theta$ of elevation of the sun when the shadow is 20 $\mathrm{ft}$ long.
Analytic Trigonometry
Inverse Trigonometric Functions
Height of a Pole $A 50$ -ft pole casts a shadow as shown in the figure. (a) Express the angle of elevation $\theta$ of the sun as a function of the length $s$ of the shadow. (b) Find the angle $\theta$ of elevation of the sun when the shadow is 20 ft long.
Trigonometric Functions: Right Triangle Approach
Inverse Trigonometric Functions and Right Triangles
Marc L.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Watch the video solution with this free unlock.
EMAIL
PASSWORD