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inna [77]
3 years ago
7

PLEASE HELP ME! :)

Mathematics
2 answers:
zepelin [54]3 years ago
8 0

NO = 6√2

MO = 3√2+3√6

mina [271]3 years ago
7 0

Answer:

1). Perimeter = 35.18 units

2). NO = 4.24 units, MO = 11.59 units

Step-by-step explanation:

1). Given : In ΔKLM,

LM = 12, m∠K = 60°, m∠M = 45°

Then we have to find the perimeter of the given triangle.

By applying sine rule in the triangle,

\frac{sinK}{LM}=\frac{sinL}{KM}=\frac{sinM}{KL}

Since ∠K + ∠L + ∠M = 180°

60 + ∠L + 45 = 180

∠L + 105 = 180

∠L = 180 - 105

∠L = 75°

\frac{sin60}{12}=\frac{sin75}{KM}

\frac{0.866}{12}=\frac{0.966}{KM}

KM = \frac{0.966\times 12}{0.866}

KM = 13.38 unit

Similarly, \frac{sinK}{LM}=\frac{sinM}{KL}

\frac{sin60}{12}=\frac{sin45}{KL}

KL = \frac{0.707\times 12}{0.866}

KL = 9.80 unit

Therefore, Perimeter of the triangle = LM + KL+ KM

= 12 + 9.80 + 13.38

= 35.18 units

2). Given in the ΔMNO,

m∠M = 45°, m∠O = 30° and MN = 6 units

To Find : Measure of NO and MO

m∠M + m∠N + m∠O = 180

45 + m∠N + 30 = 180

m∠N + 75 = 180

m∠N = 180 - 75

m∠N = 105°

Now we apply the sine rule in the triangle.

\frac{sinM}{NO}=\frac{sinN}{MO}=\frac{sinO}{MN}

\frac{sinN}{MO}=\frac{sinO}{MN}

\frac{sin105}{MO}=\frac{sin30}{6}

\frac{0.966}{MO}=\frac{0.5}{6}

MO = \frac{6\times 0.966}{0.5}

MO = 11.59 units

\frac{sinM}{NO}=\frac{sinO}{MN}

\frac{sin45}{NO}=\frac{sin30}{6}

NO = \frac{0.5\times 6}{0.707}

NO = 4.24 units

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