All categories

3 years ago

NEED IT ASAP What is the value of x in the diagram below? A.18/ ROOT 3 B.18 ROOT 2/ROOT 3 C.18 ROOT 3/ ROOT 2 D. 18 ROOT 2

Mathematics

1 answer:

Ostrovityanka [42]3 years ago

3 0

Answer:

x = B. 18 ROOT 2/ROOT 3

Step-by-step explanation:

There are two Triangles in the diagram above.

Step 1

We would solve for Triangle A First

Using Trigonometric function Cosine

cos θ = adjacent /hypotenuse

θ = 30°

Adjacent = 9 units

Hypotenuse = unknown

cos 30= 9/ Hypothenuse

Cross Multiply

cos 30 × Hypotenuse = 9

Hypotenuse = 9 / cos 30

cos 30 in surd form = √3/2

Hypotenuse = 9/√3/2

Hypotenuse = 9 × 2/√3

= 18/√3 units

Step 2

We would solve for the upper triangle = Triangle B

We are looking for x

θ = 45°

For Triangle B, the Hypotenuse we solved for in Triangle A is equivalent to the adjacent in Triangle B

Therefore ,

Hypotenuse for Triangle A = Adjacent side for Triangle B

θ = 45°

Adjacent = 18/√3 units

Hypotenuse = x = unknown

We would solve for this using Trigonometric function cosine

cos 45 = 18/√3 units / Hypothenuse

Cross Multiply

cos 45 × Hypotenuse = 18/√3 units

Hypotenuse = 18/√3 units / cos 45

cos 45 in surd form = 1/√2

Subtituting, we have

Hypotenuse (x) = 18/√3 units / 1/√2

Hypotenuse (x) = 18/√3 units ×√2/1

= 18× √2/ √3 units

= 18 √2/√3 units

Therefore x = Option B. 18 ROOT 2/ROOT 3

You might be interested in

Which relationship would most likely be casual? Select two options

Kruka [31]

The anwser is most likely a

7 0

4 years ago

Bob's Gift Shop sold 750 cards for Mother's Day. One salesman, Scarlett, sold 20% of the cards sold for Mother's Day. How many c

Semenov [28]

750*20/100
=150 cards

5 0

3 years ago

I would really appreciate it if someone helped answer these 4 questions. I will rate 5 stars. Thank you (:

ELEN [110]

Answer:

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

Recall the three main trig functions

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

( remember hypotenuse = longest side length , opposite = side length opposite of angle , and adjacent = side length thats not the opposite or hypotenuse )

We will use these to solve each problem

We are given :

An angle with a measure of 39 degrees
The angles opposite side length
The adjacent side as the unknown

When dealing with opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in opp = 11 and adj = x as well as given angle 39

tan(39) = 11/x

==> multiply both sides by x

xtan(39) = 11

divide both sides by tan(39)

x = 11/tan(39)

plugging this into a calculator , we get x = 13.6 ( rounded )

We are given :

an angle with a measure of 46 degrees
the hypotenuse which has a length of 28
and the adjacent as the unknown

When dealing with adjacent and hypotenuse we use cos

We have cos = adj / hyp

==> plug in given angle 46 , adj = x and hyp = 28

cos(46) = x/28

==> multiply both sides by 28

x = 28cos(46)

plugging this into a calculator we get x = 19.5 ( rounded )

We are given :

an angle with a measure of 51 degrees
its opposite side length with a length of 8
the adjacent side length as the unknown

When dealing with the opposite and adjacent we use tangent

We have tan = opp / adj

==> plug in 51 degrees for angle , opp = 8 and adj = x

tan(51) = 8/x

==> multiply both sides by x

xtan(51) = 8

==> divide both sides by tan(51)

x=8/tan51

plugging this into a calculator we get that x = 6.5 ( rounded )

10.

We are given:

an angle with a measure of 24 degrees
the hypotenuse which has a length of 31
the side length opposite of given angle as the unknown

When dealing with the opposite and hypotenuse we use sine

We have sin = opp / hyp

==> plug in angle as 24 , opp = x and hyp = 31

sin(24) = x / 31

==> multiply both sides by 31

31sin(24) = x

plugging this into a calculator we get that x = 12.6 ( rounded )

And we are done!

Let me know if you have any doubts in the comments ! : )

6 0

3 years ago

The local street cart sells bacon egg and cheese sandwiches for $2.50, and soft drinks for $0.75. The street vendor made a total

zaharov [31]

Answer:

Step-by-step explanation:

3 0

3 years ago

Prove that sinxtanx=1/cosx - cosx

maks197457 [2]

Answer:

See below

Step-by-step explanation:

We want to prove that

$\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}$

Taking the RHS, note

$\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}$

Remember that

$\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)$

Therefore,

$\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}$

Once

$\dfrac{\sin(x)}{\cos(x)} = \tan(x)$

Then,

$\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)$

Hence, it is proved

5 0

3 years ago