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notsponge [240]

3 years ago

8

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

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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4 0

3 years ago

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