Question

PLEASE HELP ME! :)

Answer 1

NO = 6√2

MO = 3√2+3√6

Answer 2

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