December 05 ACT Math Problem (Help Needed)

<p>So I took the December 05 ACT for practice and had a question for Math. Help with an explanation would be much appreciated.</p>

<ol>
<li>The Leaning Tower of Proville creates an 85 degree angle between itself and the level ground around the tower. The tower's shadow is 100 feet long. If it can be determined, which of the following expressions gives the distance, in feet, from the top of the tower to the ground?
A. 100 cos 85 degrees
B. 100 sin 85 degrees
C. 100 tan 85 degrees
D. 100 cot 85 degrees
E. Cannot be determined from the given information.</li>
</ol>

<p>The correct answer is E. Why is it not C?</p>

<p>if you draw a picture, you will find out that the length of the shadow and the tower dont make a right triangle</p>

<p>^But you don't know the height of the tower.</p>

<p>The height of the tower is irrelevant. The fact remains that the tower is on a slant (the tower creates an 85 degree angle with the ground, not the normal 90 degree that would one would assume for a tower. Hence the "leaning tower of proville" name). Because of this, you can't use sin/cos/tan because that can only be used for right triangles. Thus, the answer is cannot be determined.</p>

<p>^Oh, I was looking at the triangle as an 85 degree, 5 degree and 90 degree triangle. Does that not work?</p>

<p>^I don't believe so- where would the 90 degree angle be?</p>

<p>If / were the tower, and the shadow was to the left ( ....\ ), then there is no 90 degree angle (just connect the dots to the top of the slanted line). If it's to the right ( ...), then the angle between the ground and the building would no longer be 85 degrees, it would be 95 degrees, making it impossible for another angle within the triangle to be 90 degrees.</p>

<p>^You're right, I should have drawn a picture when I was actually doing this problem. Thanks for the help. :)</p>

<p>^No problem :)</p>