Because there are 6 letters in WINNER, you can use factorials to find out how many ways the letters can be arranged.
Factorials are represented with the ! symbol. Use the factorial of 6 to solve the problem:
There are
720 different ways the letters can be arranged.
Answer:
h = 5(tane)
Step-by-step explanation:
The diagrammatic representation of the question given is attached below ;
The height of the light pole, h = opposite side
Adjacent side = 5 feets
Angle of elevation = e
Using trigonometry ;
Tan e = opposite / Adjacent
Tan e = h / 5
Making h the subject ;
h = 5(tane)
Angle-5 and angle-7 are 'vertical angles', so they're equal,
and we can write ...
<u>10x- 9 = 9x</u>
Subtract 9x from each side: x - 9 = 0
Add 9 to each side: <u> x = 9</u>
Now that we know what 'x' is, we can find the size of Angles-5 and -7 .
Angle-7 = 9x = 81° .
Now look at Angle-6 ... the one that's the answer to the problem.
Angle-6 and -7 together make a straight line, so they must
add up to 180°.
<u>Angle-6 + 81° = 180°</u>
Subtract 81° from each side: Angle-6 = <em>99° .</em>
1/5 = 3/4 miles
multiply 3/4 by 5
The relay is 15/4 miles