A 35-foot tall pole is leading towards a building. To stop the pole from leaning
1 answer:
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Answer:
38.5°
Step-by-step explanation:
You are given all three side lengths of the relevant triangle, so the Law of Cosines can be used to find any desired angle. If we call the desired angle C, then that law tells you ...
C = arccos((a² +b² -c²)/(2ab))
where a and b are the triangle side lengths adjacent to the angle of interest, and c is the side opposite. Here, 'a' and 'b' are the pole and cable lengths, and 'c' is the distance of the stake from the pole.
C = arccos((35² +48² -30²)/(2·35·48)) = arccos(2629/3360)
C ≈ 38.515°
The cable makes an angle of about 38.5° with the pole.
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Answer:
9 inches.
Step-by-step explanation:
Fun question! The length of a space diagonal for a cube is
Thus, the first cube has a side diagonal of
The next cube would have a side diagonal of 3
The third cube would have a side diagonal of
And the fourth cube would have a side diagonal of 9.
Since the fifth cube has a side length equal to the side diagonal of the fourth cube, it should be 9 inches.
Given the equation:
(a) You can identify that the student applied the Subtraction Property of Equality by subtraction 3 from both sides of the equation:
However, the student made a mistake when adding the numbers on the right side.
Since you have two numbers with the same sign on the right side of the equation, you must add them, not subtract them and use the same sign in the result. Then, the steps to add them are:
- Add their Absolute values (their values without the negative sign).
- Write the sum with the negative sign.
Then:
(b) The correct procedure is:
1. Apply the Subtraction Property of Equality by subtracting 3 from both sides (as you did in the previous part):
2. Apply the Multiplication Property of Equality by multiplying both sides of the equation by 6:
Hence, the answers are:
(a) The student made a mistake by adding the numbers -18 and -3:
(b) The value of "x" should be: