What is 9.105 rounded to the nearest hundredth
1 answer:
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Answer:
The height of the light pole to the nearest foot is approximately 50 feet
Step-by-step explanation:
The parameters given in the question are;
The length of the cable = 63 feet
The angle of elevation of the cable to the top of the light pole = 52°
With the assumption that the light pole is perpendicular to the ground, the figure formed by the light pole, the distance of the of the cable from the base of the light pole and the length of the cable form a right triangle
The question can be answered by using trigonometric relations for the sine of the given angle as follows;
The opposite leg length of the formed right triangle = The height of the light pole
The hypotenuse length = The length of the cable = 63 feet
The angle, θ = The angle of elevation = 52°
Plugging in the values, gives;
∴ The height of the light pole = 63 feet × sin(52°) ≈ 49.645 feet
The height of the light pole to the nearest foot ≈ 50 feet.
Answer:
(40,0)
Step-by-step explanation:
A rotation of 270 degrees° counterclockwise about the origin has the rule
A ferris wheel is drawn on a coordinate plane so that the first car is located at the point (0,40).
According to the given rule, the image point after a rotation of 270 degrees° counterclockwise about the origin have the coordinates (40,0) (see attached diagram for details).
The parallel sides AB, PQ, and CD, gives similar triangles, ∆ABD ~ ∆PQD and ∆CDB ~ ∆PQB, from which we have;
From the given information, we have;
- ∆ABD ~ ∆PQD
- ∆CDB ~ ∆PQB
According to the ratio of corresponding sides of similar triangles, we have;
Which gives;
QD × x = BD × z
BD × z = (1 - QD/BD) × y = y - (QD × y/BD)
Therefore;
BD × z = y - (QD × y/BD)
BQ × y = y - (QD × y/BD)
BQ × y = y - (z × y/x) = y × (1 - z/x)
(1 - z/x) = BQ
BD × z = y × (1 - z/x)
BD = (y × (1 - z/x))/z
Therefore;
QD × x = y × (1 - z/x)
(BD-BQ) × x = y × (1 - z/x)
(BD-(1 - z/x)) × x = y × (1 - z/x)
BD = (y × (1 - z/x))/x + (1 - z/x)
BQ + QD = (1 - z/x) + (y × (1 - z/x))/x
BD = BQ + QD
(y × (1 - z/x))/x + (1 - z/x) = (y × (1 - z/x))/z
(1 - z/x)×(y/x + 1) =(1 - z/x) × y/z
Dividing both sides by (1 - z/x) gives;
y/x + 1 = y/z
Dividing all through by y gives;
(y/x + 1)/y = (y/z)/y
- 1/x + 1/y = 1/z
Therefore;
Learn more about characteristics similar triangles here:
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