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lutik1710 [3]
3 years ago
10

Help with practice problem

Mathematics
1 answer:
padilas [110]3 years ago
5 0

Answer:

attached above with detail explanation.

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In right triangle LMN, L and M are complementary angles and sin(L) is 19/20. What is cos(M).
Juliette [100K]

Option A:

$\cos M=\frac{19}{20}

Solution:

The image of the triangle is attached below.

Given data:

$\sin L=\frac{19}{20}

Using trigonometric ratio formulas,

$\sin L=\frac{\text { Opposite side of } L}{\text { Hypotenuse }}

$\sin L=\frac{MN}{LM}

So, MN = 19 and LM = 20

Using Pythagoras theorem,

In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.

LM^2=LN^2+MN^2

20^2=LN^2+19^2

400=LN^2+361

Subtract 361 from both sides,

39 = LN²

Taking square root on both sides,

LN=\sqrt{39}

$\cos \theta=\frac{\text { Adjacent side of } \theta}{\text { Hypotenuse }}

$\cos M=\frac{\text { Adjacent side of } M}{\text { Hypotenuse }}

$\cos M=\frac{MN}{LM}

$\cos M=\frac{19}{20}

Hence option A is the correct answer.

7 0
4 years ago
Eight less than four times a number is less than 56. What are the possible<br> Values of that number
Ivan

Answer:

Step-by-step explanation:

If you would like to write the following in the math expression, you can do this using these steps:

a number ... n

eight less than four times a number ... 4 * n - 8

is less than 56 ... < 56

4 * n - 8 < 56

4 * n < 56 + 8

4 * n < 64     /4

n < 64 / 4

n < 16

The possible values of that number are less than 16.

7 0
3 years ago
There are 15 boys and 13 girls in Mr. Garcia's class. What is the ratio of girls to boys?
nordsb [41]

Answer: 13:15

Step-by-step explanation:

6 0
3 years ago
I need to find all the angles but i don’t understand plz help
devlian [24]
A = 121, Vertical Angles Theorem
B = 59, Supplementary Angles Theorem
C = 59, Vertical Angles Theorem
D = 55, Alternate Interior Angles Theorem
E = 4, sum of all angles in a triangle is 180
F = 73, sum of all angles in a triangle is 180
G = 73, Alternate Interior Angles Theorem
H = 48, Alternate Interior Angles Theorem
I = 4, Alternate Interior Angles Theorem
3 0
3 years ago
How many permutations of the word spell are there
SOVA2 [1]
120 should be the answer
4 0
3 years ago
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