A highway curve forms a section of a circle. A car goes around the curve as show

Question

A highway curve forms a section of a circle. A car goes around the curve as shown in the helicopter view in the figure below. Its dashboard compass shows that the car is initially heading due east. After it travels

d = 855 m,

it is heading

= 34.5°

south of east. Find the radius of curvature of its path. Suggestion: Use

s = r

where is in radians.

A high fountain of water is located at the center of a circular pool as shown in the figure below. A student walks around the pool and measures its circumference to be 38.2 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation of the top of the fountain to be = 60.0°. How high is the fountain?

You first need to find the distance from the student to the center of the fountain. Then you can use trigonometry to find the height. m

Explanation / Answer

2.

A high fountain.....

Ans:

Circumference of pool = C = 2*pi*r

r = C/2*pi

r = 38.2/(2*pi) = 6.08 m

Height of fountain = h

than

tan phi = h/r

h = r*tan phi

using given values

h = 6.08*tan 60 deg = 10.53 m

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