When viewing Angel Falls (the world's highest waterfall) from Observation Platform A, located on the same level as the bottom of the waterfall, we calculate the angle of elevation to the top of the waterfall to be 69.30°. From Observation Platform B, which is located on the same level exactly 1000 feet from the first observation point, we calculate the angle of elevation to the top of the waterfall to be 52.90°. How high is the waterfall?
A. 2,646 ft
B. 998.5 ft
C. 1,322 ft (my answer)
D. 2,643 ft
A carpenter wants to be sure that the corner of a building is square and measures 6.0 ft and 8.0 ft along the sides. How long should the diagonal be?
A. 12 ft (my answer)
B. 14 ft
C. 11 ft
A. 2,646 ft
B. 998.5 ft
C. 1,322 ft (my answer)
D. 2,643 ft
A carpenter wants to be sure that the corner of a building is square and measures 6.0 ft and 8.0 ft along the sides. How long should the diagonal be?
A. 12 ft (my answer)
B. 14 ft
C. 11 ft
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(1). The bottom of the waterfalls (F), the top (T), observation point A (A) and point B (B) would form two right/angle triangles when drawn out with triangle TFA inside triangle TFB; TF being vertical, BT being the outer hypotenuse and BF being the total base.
The distance between observation point A and B is 1000 feet.
* taking the tangent of angle TAF*
tan (69.30) = |TF| / |AF|
2.6464 = |TF| / |AF|
=> |AF| = |TF| / 2.6464
=> |AF| = 0.3779|TF|
*taking the tangent of angle TBF*
tan (52.90) = |TF| / |BF|
1.3222 = |TF| / |BF|
|BF| = |TF| / 1.3222
=> |BF| = 0.7563 |TF|
|BF| = |BA| + |AF|
0.7563|TF| = 1000 + 0.3779|TF|
0.7563|TF| - 0.3779|TF| = 1000
0.3784|TF| = 1000
|TF = 1000 / 0.3784
|TF| = 2642.71 feet = 2643 ft.
(2). Let the diagonal be D.
* using pythagoras theorem*
D^2 = 6^2 + 8^2
D^2 = 36 + 64
D^2 = 100
D = sqrt 100 = 10
The distance between observation point A and B is 1000 feet.
* taking the tangent of angle TAF*
tan (69.30) = |TF| / |AF|
2.6464 = |TF| / |AF|
=> |AF| = |TF| / 2.6464
=> |AF| = 0.3779|TF|
*taking the tangent of angle TBF*
tan (52.90) = |TF| / |BF|
1.3222 = |TF| / |BF|
|BF| = |TF| / 1.3222
=> |BF| = 0.7563 |TF|
|BF| = |BA| + |AF|
0.7563|TF| = 1000 + 0.3779|TF|
0.7563|TF| - 0.3779|TF| = 1000
0.3784|TF| = 1000
|TF = 1000 / 0.3784
|TF| = 2642.71 feet = 2643 ft.
(2). Let the diagonal be D.
* using pythagoras theorem*
D^2 = 6^2 + 8^2
D^2 = 36 + 64
D^2 = 100
D = sqrt 100 = 10
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Here's a hint for the first question: The structure is a triangle ABC with a base of 1000 ft. You calculate the remaining angle (remember, the total degrees of a triangle add up to 180 degrees). Then, use the Law of Sines to calculate the lengths of the two sides. Then, using the Law of Sines again, as well as the definition of the sine of an angle, calculate the height of the waterfall. For this part, check out "Derivation" under the Wikipedia link for an illustration.
For the second question, I didn't get any of the answers. You add the square of the length and the square of the width, then take the square root of the sum.
For the second question, I didn't get any of the answers. You add the square of the length and the square of the width, then take the square root of the sum.
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sorry, no answer.
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Sorry don't get it.