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Makovka662 [10]
3 years ago
8

Does anyone know this

Mathematics
1 answer:
Phantasy [73]3 years ago
4 0

The value of x is 20.

Solution:

Sides of one triangle are 2x – 4 and 39.

Sides of another triangle are x + 6 and 24.

<u>Property of similar triangle:</u>

<em>If two triangles are similar then their corresponding angles are congruent and the corresponding sides are in the same ratio.</em>

$\frac{2x-4}{24} =\frac{39}{x+6}

Do cross multiplication.

(2x-4)(x+6)=39\times 24

2x^2+12x-4x-24=936

2x^2+8x-24-936=0

2x^2+8x-960=0

Divide by 2 on each of the term.

x^2+4x-480=0

Solve using quadratic equation.

(x-20)(x+24)=0

(x-20)=0, \ (x+24)=0

x = 20,  \ x = -24

Ignore the negative term, because if you substitute this you will get a negative terms only. But length of sides cannot be in negative measures.

Therefore x = 20.

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Cos(x) = sin(x + 20o) Use the double cos angle formula

Cos(x) = sin(x)*cos(20) + cos(x)*sin(20) Divide through by cos(x). Tanx = sin(x)/cos(x)

1 = tan(x)*cos(20) + sin(20) Subtract sin(20) from both sides.

1 - sin(20) = tan(x)*cos(20) Calculate the value of 1 - sin(20)

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x = 35 degrees as expected.

Problem Two

The easiest way to do this is to pick random values and try it. The two acute angles are complementary. So 25 and 65 are random enough.

Let A = 25

Let C = 65

A

Tan(25) = sin(25)/sin(65) ; tan(25) = 0.4663.

sin(25)/sin(65) = 0.4663 Answer

B

Sin(90 - C) = Sin(A)

Tan(90 - A) = Tan(C)

So the question becomes Cos(A) = Tan(C) / sin(A)

Cos(25) = Tan(65)/Sin(25)

0.906 = ? 5.07 This statement isn't true.

C

Sin(65) = Cos(25)/Tan(65)

.906 = 0.4226 C is not the correct answer.

D

D isn't true. The tan does not relate that away. You can find it for yourself.

Cos(A) = Tan(C) You should get 0.906 = 2.14

E

Sin(C) = Cos(A) / Tan(A) I'll leave you to show this is wrong.

Problem 3

The diagram below is for this problem. Cos(x) = 50/100 = 0.5

x = cos-1(0.5)

x = 60 degrees.

Part 2

Sin(60) = opposite / hypotenuse

opposite = sin(60) * hypotenuse

opposite = 86.61 Be sure and round this to whatever the question says to round it to.



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