Answers:
- Y = 176.0 feet
- X = 128.7 feet
Note: Your teacher may not want you to type "feet" into the answer boxes.
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Explanation:
The tree's shadow is 120 ft long, so it's the length of the horizontal side of the triangle. With regard to the reference angle (47 degrees), this 120 ft side is adjacent to the angle because it's as close as possible to the angle. That means the X is the opposite side of the reference angle.
The Y side is the longest side. It's the hypotenuse. The hypotenuse is always the longest side and always opposite the largest angle of a right triangle (so it's always opposite the 90 degree angle).
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To find Y, we'll use the cosine rule
cos(angle) = adjacent/hypotenuse
cos(47) = 120/Y
Y*cos(47) = 120
Y = 120/cos(47)
Y = 175.9535 .... make sure your calc is in degree mode
Y = 176.0
When rounding to the nearest tenth, the second '5' will bump that 9 up to 10, which then carries over and why 175 bumps up to 176.
The distance from the tip of the tree to the tip of the shadow is roughly 176 feet.
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We can use the tangent rule to find X
tan(angle) = opposite/adjacent
tan(47) = X/120
120*tan(47) = X
X = 120*tan(47)
X = 128.6842
X = 128.7
The tree is roughly 128.7 feet tall
This is somewhere between a 12 story and 13 story building assuming each story is 10 ft (since 12 stories = 12*10 = 120 ft, and 13 stories = 130 ft).
