I need step by step instructions on this math problem?
http://smragan.com/tag/overengineered/ A giant redwood tree casts a shadow 532 feet long when the angle of elevation to the sun is 26 degrees. Find the height of the tree to the nearest tenth of a foot.
I need step by step instructions, not just the answer! I’d like to understand how to work the problem.
Thanks in advance!
3 Responses
trueprober
26 May 2011
Mambojevi
26 May 2011
Think of this as a triangle, with the bottom of the triangle being the shadow and the side being the tree. So you have two sides of a triangle, you are provided with the opposite and need to solve for the adjacent. You are provided the angle.
So with the information you have, the opposite and the angle, you can solve for the adjacent. This is found by using the tangent function.
Tangent theta = opposite over the adjacent.
Theta = angle.
Tan 26 = 532/ adjacent
So 532 tan 26 = adjacent = 259.47 ft
D.W.
26 May 2011
Let the tip of the shadow be at the origin.
The base of the tree is at (532, 0).
Slope of a ray of sunlight = tan(26°) = 0.487733
Equation for the ray of light passing through the tip of the shadow:
y = 0.48773x
Height of tree = 0.48773·532 ≅ 259.5 feet
Hi Dearly beloved~, as you say the angle of elevation is 26 degree, then we draw a right angled triangle with 26 degree at the bottom. Now the shadow would be the adjacent side and the actual tree would be the opposite side for angle 26 deg.
Hence tan 26 = opp side / adj side
Hence tan 26 = h / 532. Here h is the required height of the tree to be found.
So h = 532 tan 26
Using tables or calculator you yourself can find the value of h.