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notsponge [240]
3 years ago
8

Given: △FKL, FK= a m∠F=45°, m∠L=30° Find: FL

Mathematics
1 answer:
mr Goodwill [35]3 years ago
6 0

The sum of angles of a triangle is 180°, so m∠K = 180° -45° -30° = 105°.

The Law of Sines tells you

... FL/sin(∠K) = FK/sin(∠L)

Solving for FL, we get

... FL = FK·sin(∠K)/sin(∠L)

... FL = a·sin(105°)/sin(30°) = a·sin(105°)/(1/2)

... FL = 2a·sin(105°) ≈ 1.93185a

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Put the correct answer in each blank.
serious [3.7K]

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H or (3.5,-3)

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4 0
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Help based offf order of operations please help
JulijaS [17]

Answer:

The answer for :

h. \:  \:   \: \frac{5}{6}

i. \:  \:  \:  \frac{35}{32}

k. \:  \:  \:  \frac{-29}{20}

l. \:  \:  \:  \frac{13}{15}

Step-by-step explanation:

Question h:

\frac{2}{3}  + ( \frac{1}{3}  \times  \frac{1}{2} )

=  \frac{2}{3}  +  \frac{1}{6}

=  \frac{2 \times 2}{3 \times 2}  +  \frac{1}{6}

=  \frac{4}{6}  +  \frac{1}{6}

=  \frac{5}{6}

Question i:

\frac{7}{8}  +  \frac{1}{4}  \times ( \frac{3}{2}  -  \frac{5}{8} )

=  \frac{7}{8}  +  \frac{1}{4}  \times ( \frac{3 \times 4}{2 \times 4}  -  \frac{5}{8} )

= \frac{7}{8}  +  \frac{1}{4}  \times ( \frac{12}{8}  -  \frac{5}{8} )

=  \frac{7}{8}  +  (\frac{1}{4}  \times  \frac{7}{8} )

=  \frac{7}{8}  +  \frac{7}{32}

=  \frac{7  \times 4}{8 \times 4}  +  \frac{7}{32}

=  \frac{28}{32}  +  \frac{7}{32}

=  \frac{35}{32}

Question k:

\frac{3}{4}  - ( \frac{12}{7}  \div  \frac{12}{21} ) +  \frac{4}{5}

=  \frac{3}{4}  - ( \frac{12}{7}  \times  \frac{21}{12} ) +  \frac{4}{5}

=  \frac{3}{4}  -  \frac{3}{1}  +  \frac{4}{5}

= \frac{3 \times 5}{4 \times 5}  -  \frac{3 \times 20}{1 \times 20} +  \frac{4 \times 4}{5 \times 4}

=  \frac{15}{20}   -   \frac{60}{20} +  \frac{16}{20}

=  -  \frac{29}{20}

Question l:

\frac{5}{2}  \times ( \frac{2}{3}  -  \frac{1}{5} ) - ( \frac{2}{5}  \div  \frac{4}{3} )

=  \frac{5}{2}  \times ( \frac{2 \times 5}{3 \times 5}  -  \frac{1 \times 3}{5 \times 3} ) - ( \frac{2}{5}  \times  \frac{3}{4} )

=  \frac{5}{2}  \times ( \frac{10}{15}  -  \frac{3}{15} ) -  \frac{3}{10}

=  (\frac{5}{2} \times   \frac{7}{15}) -  \frac{3}{10}

=  \frac{7}{6}  -  \frac{3}{10}

=  \frac{7 \times 5}{6 \times 5}  -  \frac{3 \times 3}{10 \times 3}

=  \frac{35}{30}  -  \frac{9}{30}

=  \frac{26}{30}

=  \frac{13}{15}

8 0
3 years ago
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