Posted by admin | Posted in trees,shrubs | Posted on 30-06-2009
Tags: christmas, christmas trees missouri, christmas trees missouri valley, farm, missouri, photo, sharing
Help with these summer physics problems?
The silhouette of a Christmas tree is an isosceles triangle. The angle at the top of the triangle is 20.0°, and the base measures 1.20 m across. How tall is the tree?
You are driving into St. Louis, Missouri, and in the distance you see the famous Gateway-to-the-West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 2.3° above the horizontal. Approximately how far (in kilometers) are you from the base of the arch?
detail on why would be helpful as well 
If you draw a line from the top of the tree to the base and perpendicular to it and examine just one side, you’ll have a triangle with a 10.0° angle (half of the 20.0° we split in two), a 90.0° angle (formed by the line we drew perpendicular to the base, and the base), and a side of 0.60m (one half of 1.20m, opposite side of our triangle). From the definition of the tangent ratio, the adjacent side (our height) may be found:
tanθ = opposite side / adjacent side
adjacent side = opposite side / tanθ
= 0.60m / tan10.0°
= 3.40m
You use the same trig ratio (tangent) for the arch problem. The height of the arch is your opposite side, so:
distance (adjacent side) = height (opposite side) / tanθ
= 192m / tan2.30°
= 4780m (4.78km)
Hope this helps.
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