All categories

3 years ago

Find the length of LM. Show your work.

Mathematics

1 answer:

Fantom [35]3 years ago

7 0

Answer:

LM = 20

Step-by-step explanation:

Use the Sine rule to calculate the length of LM

We require to find ∠N using sum of angles in a triangle.

∠N = 180° - (53 + 44)° = 180° - 97° = 83°, then

$\frac{LN}{sin44}$ = $\frac{LM}{sin83}$ ( cross- m ultiply )

LM × sin44° = LN × sin83°, that is

LM × sin44° = 14 × sin83° ( divide both sides by sin44° )

LM = $\frac{14sin83}{sin44}$ = 20

You might be interested in

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side

lorasvet [3.4K]

Answer:

Step-by-step explanation:

cot x sec⁴ x = cot x+2 tan x +tan³x

L.H.S = cot x sec⁴x

=cot x (sec²x)²

=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]

= cot x(1+ 2 tan²x +tan⁴x)

=cot x+ 2 cot x tan²x+cot x tan⁴x

=cot x +2 tan x + tan³x [ ∵cot x tan x $=\frac{ \textrm{tan x }}{\textrm{tan x}}$ =1]

=R.H.S

(sin x)(tan x cos x - cot x cos x)=1-2 cos²x

L.H.S =(sin x)(tan x cos x - cot x cos x)

= sin x tan x cos x - sin x cot x cos x

$=\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}$

= sin²x -cos²x

=1-cos²x-cos²x

=1-2 cos²x

=R.H.S

1+ sec²x sin²x =sec²x

L.H.S =1+ sec²x sin²x

= $1+\frac{{sin^2x}}{cos^2x}$ [ $\textrm{sec x}=\frac{1}{\textrm{cos x}}$ ]

=1+tan²x $[\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}]$

=sec²x

=R.H.S

$\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}$

L.H.S= $\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}$

$=\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}$

$=\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}$

$=\frac{\textrm{2sin x}}{sin^2 x}$

= 2 csc x

= R.H.S

-tan²x + sec²x=1

L.H.S=-tan²x + sec²x

= sec²x-tan²x

= $\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}$

$=\frac{1- sin^2x}{cos^2x}$

$=\frac{cos^2x}{cos^2x}$

8 0

3 years ago

9,261.95 x 0.003= ?<br><br> Plzz help

IgorLugansk [536]

Answer:

27.78585

Step-by-step explanation:

4 0

3 years ago

Explain what a variable is

AleksAgata [21]

A variable is a letter that replaces an unknown number.

7 0

2 years ago

12. A family spends 1 hours traveling to a theme park, 6 hours at the

Rasek [7]

Answer:

4 hours

Step-by-step explanation:

1+1=2

6-2=4

6 0

3 years ago

Read 2 more answers

Which choice best represents the balance of a savings account at the end of 6 years if the simple interest earned each year is 6

Amiraneli [1.4K]

Answer:

$507.00.

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 6.5%/100 = 0.065 per year,

then, solving our equation

I = 1300 × 0.065 × 6 = 507

I = $ 507.00

The simple interest accumulated

on a principal of $ 1,300.00

at a rate of 6.5% per year

for 6 years is $ 507.00.

4 0

2 years ago