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the tree below casts a shadow that is 24 feet long, and the angle of
elevation from the tip of the shadow to the top of the tree has a cosine of . what is the height of the
tree?
title
tree casting a shadow
your result
correct
difficulty
hard
your pace
0:01
others' pace
1:24
video explanation
text explanation
the answer is b. the cosine tells us the ratio of the adjacent side of the angle to the hypotenuse.
remember the mnemonic sohcahtoa, which helps us remember the trig function ratios for right triangles.
since we know the ratio of the adjacent side to the hypotenuse and we know the length of the adjacent side we can find the length of the hypotenuse by setting up a proportion:
cross-multiplying, we find that 4x = 120 so x = 30. so the hypotenuse of the triangle is 30, but remember we are looking for the height of the tree. we can use the pythagorean theorem, a2 + b2 = c2 to find this:
242 + y2 = 302
y2= 324
y = 18 (the height of the tree)
if you recognized from the beginning that we have a 3-4-5 triangle, you could skip the initial step of finding the hypotenuse and use the tangent to set up a proportion to find the height of the tree:
related lessons
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