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Alika [10]
3 years ago
5

A tennis court is 78 feet long and 36 feet wide. If a player hits the ball diagonally from one corner to the diagonal corner on

the opposite side, how many feet has it crossed on the court? (Round your answer to the nearest whole number)
Mathematics
1 answer:
12345 [234]3 years ago
8 0
The line cutting the rectangle diagonally gives you two identical triangles and the dividing line is the hypotenuse.

So we apply the Pythagorean formula:
a^2+b^2 = c^2
36^2+78^2 = c^2
1296+6084 = 7380 take the square root: sqrt7380 = 85.9


Answer 85.9 feet = round to 86
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Work Shown:

Find the first term of the sequence by plugging in n = 1

a_n = (5/6)*n + 1/3

a_1 = (5/6)*1 + 1/3    replace n with 1

a_1 = 5/6 + 1/3

a_1 = 5/6 + 2/6

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Repeat for n = 58 to get the 58th term

a_n = (5/6)*n + 1/3

a_58 = (5/6)*58 + 1/3    replace n with 58

a_58 = (5/6)*(58/1) + 1/3

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a_58 = 290/6 + 1/3

a_58 = 145/3 + 1/3

a_58 = 146/3

Now we can use the s_n formula below with n = 58

s_n = (n/2)*(a_1 + a_n)

s_58 = (58/2)*(a_1 + a_58)    replace n with 58

s_58 = (58/2)*(7/6 + a_58)   replace a_1 with 7/6

s_58 = (58/2)*(7/6 + 146/3)   replace a_58 with 146/3

s_58 = (58/2)*(7/6 + 292/6)

s_58 = (58/2)*(299/6)

s_58 = (58*299)/(2*6)

s_58 = 17342/12

s_58 = 8671/6


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