SOLUTION: HOW CAN I DO THIS WITHOUT A CALCULATOR? A giant redwood tree casts a shadow, as shown in the figure. (Hint: tan25.7 = 0.4817) (A) If the shadow casted is 532 At long, and if the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: HOW CAN I DO THIS WITHOUT A CALCULATOR? A giant redwood tree casts a shadow, as shown in the figure. (Hint: tan25.7 = 0.4817) (A) If the shadow casted is 532 At long, and if the      Log On


   

Question 1189019: HOW CAN I DO THIS WITHOUT A CALCULATOR?
A giant redwood tree casts a shadow, as shown in the figure. (Hint: tan25.7 = 0.4817)
(A) If the shadow casted is 532 At long, and if the angle of elevation of the sun is 25.7°, then the height of the tree
approximately equals to 378 ft.
(B) If the angle of elevation of the sun is 48.5°, the height of the tree is 256 ft, then the shadow casted is approximately
312 ft.
(C) If the angle of elevation of the sun is 36.8°, the shadow casted is 312 ft then the height of the tree is approximately
432 ft.
(D) None of the above (A) (B) (C) is correct
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.

With high probability,  THERE  IS  a calculator in your computer,
you simply do not know where to find it.


Look at the  " START "  window in your computer,  if it is  Microsoft  Windows operation system.


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comment from student: I know, but im just not allow to use a calculator at school


My response : OK, now I better understand the assignment.


Let's think logically. 


Statement (A). "If the shadow casted is 532 long, and if the angle of elevation of the sun is 25.7°, 
then the height of the tree approximately equals to 378 ft."


    We are given tan(25.7°) = 0.4817.

    For the height of the three, we have the formula

        h = shadow*tan(25.7°) = 532*0.4817

    Value 0.4818 is close to 0.5 (slightly less), so the formula (1) should give  the value about half of 532, i.e. about 260;

    but the statement says it is about 378 ft, which is, OBVIOUSLY, far away from the expected value.


    So, the statement (A) is incorrect - - - we should decline it . . . 


Same or similar logic should work in other cases - - - TRY IT . . . 




For example, for statement (B), the angle 48.5° is close to 45°;  so, tan(48.5°) is close to 1;

the height of the tree 256 ft (given) should be close to the shadow length, but it is not the case.


So, statement (B) is FALSE, too.




In case (C), elevation angle of 36.8° is less than 45°, so we can expect that the shadow is longer than the height,

but given data contradicts it.  So, statement (C) is FALSE, too.



Thus the answer to the problem's question is (D), and I explained you WHY.

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Solved,  answered and explained.


It is how the  COMMON  SENSE  works . . .