More Angles of Elevation and Depression (Ayers Rock)

[bookworm396]

Ulura or Ayers Rock is a sacred place for Aborigines of the western desert of Australia. Chun-Wei uses a surveying device to measure the angle of elevation to the top of the rock to be 11.5 degrees. He walks half a mile closer and measures the angle of elevation to be 23.9 degrees. How high is Ayers Rock in feet?

 

[stapel]

Ulura or Ayers Rock is a sacred place for Aborigines of the western desert of Australia. Chun-Wei uses a surveying device to measure the angle of elevation to the top of the rock to be 11.5 degrees. He walks half a mile closer and measures the angle of elevation to be 23.9 degrees. How high is Ayers Rock in feet?

Where are you stuck? You drew the two nested right triangles, labelled the distance between the two on-ground non-right angles' vertices, labelled these angles with the given angle measures, labelled the height (that you're trying to find) as "h", formed the tangent ratios, and... then what?

Please be complete. Thank you!

Eliz.

 

[tkhunny]

x is the total distance in feet from the point of the first measurement to the point directly under the highest point of Uluru.
y is the height of Uluru

\(\displaystyle \tan(11.5\;degrees)\;=\;\frac{y}{x}\)

\(\displaystyle \tan(23.9\;degrees)\;=\;\frac{y}{x-2640 ft}\)