Multiply the following binomials (X+5) (X-5)

Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Mice21 [21]

Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

Also

$m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$ (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

So,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$

3 0

3 years ago

Read 2 more answers

2a ³+10=26<br> Show the work on how you got it

Usimov [2.4K]

Answer:

a=2

Step-by-step explanation:

subtract 10 from both sides

2a^3=26-10

simplify

2a^3=16

Divivde both side by 2

a^2=16/2

simplify

a^3=8

4 0

3 years ago

Help meeeeeeeeeeeeeeeweeeeeeeeeeeeeeeee

Yuri [45]

Step-by-step explanation:

This can be put into fractions like this

Say x is the length of the missing dimension

8.5/11 = 10.5/x

Because the 2 drawings are SIMILAR, the ratio of their side lengths has to also be the same

8.5 ÷ 10.5 = 0.8095

11 × 0.8095 = 8.9047

Roung the answer to the nearest tenth

x = 8.9 in

5 0

3 years ago

Andrea ran 4 3/8 miles on

MrRissso [65]

(4 3/8) + (5 1/3)

(4+5)(3/8 + 1/3)

9 + (17/24)

she ran 9 17/24 miles total

8 0

3 years ago

ILL GIVE BRAINLIEST 25 POINTS

sashaice [31]

Answer:

Step-by-step explanation:

You shift up and down when there is a value at the end of the function outside of the parentheses. Since it is -1, you shift down one.

You shift left and right when there is a value inside the parentheses. Since it is 2, you shift left 2. Remember that you always shift left if the number positive and you shift right when it is negative.

4 0

2 years ago