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3 years ago

Solve for the variable when the hypotinuse is 10 and you know one angle, 42

Mathematics

1 answer:

Serga [27]3 years ago

3 0

Answer: The other sides are 6.7 units and 7.4 units

Step-by-step explanation: Every right angled triangle can be solved by use of the trigonometric ratios. We can use the sine, cosine or tangent depending on which sides are given. If one angle has been given as 42 degrees, then the side opposite that angle can be calculated as,

Sin 42 = opposite/hypotenuse

Sin 42 = a/10

We cross multiply and we now have

Sin42 x 10 = a

0.6691 x 10 = a

a = 6.69 (which is approximately 6.7)

If one of the other two angles was given as 42, then the third angle would be calculated as 180 - (90 + 42) {sum of angles in a triangle equals 180} and that equals 48.

To calculate the third side,

Sin48 = opposite/hypotenuse

Sin48 = y/10

We cross multiply and we have

Sin48 x 10 = y

0.7431 x 10 = y

y = 7.43 (which is approximately 7.4)

Therefore the two other sides are 6.7 and 7.4

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Festus bought a computer at $736.34, Apple iPad at $249.99, and a printer at 381.23. The sales tax rate is %6. What is the total

tatuchka [14]

The total purchase price including sales tax will be $1449.6136

Explanation

Festus bought a computer at $736.34, Apple iPad at $249.99 and a printer at $381.23

So, the total price of all three items $=(736.34+249.99+381.23) dollar = 1367.56$ dollar.

The sales tax rate is 6%. So, the amount of sales tax $=(1367.56*0.06) dollar= 82.0536$ dollar.

Thus, the total purchase price including sales tax will be: (1367.56 + 82.0536) dollar = 1449.6136 dollar

6 0

3 years ago

Ví dụ 1.5. Một người đi mua hàng 3 lần. Xác suất lần đầu mua được hàng tốt là 0,7.

vodka [1.7K]

Answer:

a) 0.50575,

b) 0.042

Step-by-step explanation:

Example 1.5. A person goes shopping 3 times. The probability of buying a good product for the first time is 0.7.

If the first time you can buy good products, the next time you can buy good products is 0.85; (I interpret this as, if you buy a good product, then the next time you buy a good product is 0.85).

And if the last time I bought a bad product, the next time I bought a good one is 0.6. Calculate the probability that:

a) All three times the person bought good goods.

P(Good on 1st shopping event AND Good on 2nd shopping event AND Good on 3rd shopping event) =

P(Good on 1st shopping event) *P(Good on 2nd shopping event | Good on 1st shopping event) * P(Good on 3rd shopping event | 1st and 2nd shopping events yield Good) =

(0.7)(0.85)(0.85) =

0.50575

b) Only the second time that person buys a bad product.

P(Good on 1st shopping event AND Bad on 2nd shopping event AND Good on 3rd shopping event) =

P(Good on 1st shopping event) *P(Bad on 2nd shopping event | Good on 1st shopping event) * P(Good on 3rd shopping event | 1st is Good and 2nd is Bad shopping events) =

(0.7)(1-0.85)(1-0.6) =

(0.7)(0.15)(0.4) =

0.042

5 0

3 years ago

What are the values of sin α and tan α, if: cosα=0.6

olganol [36]

Positive cosine is first or fourth quadrant. So we don't know the sign of the sine or the tangent.

Everybody's favorite right triangle is 3/4/5 and here we have

$\left(\dfrac 3 5 \right)^2 + \left(\dfrac 4 5 \right)^2 = 1$

So if

$\cos \alpha = 0.6 = \dfrac 3 5$

then

$\sin \alpha = \pm \dfrac{4}{5} = \pm 0.8$

and

$\tan \alpha = \dfrac{\sin \alpha}{\cos \alpha} = \dfrac{\pm 0.8}{0.6}=\pm \dfrac 4 3$

6 0

3 years ago

Find the solution for the system of equations y=4x+12 Y=6x+8

madam [21]

-12=4x-y
(-8=6x-y)-1

-12=4x-y
8=-6x+y

-4=-2x
/-2 /-2
2=x

Y=6(2)+8
Y=20

(2,20)

5 0

2 years ago

Jean closet is having a 15% off storewide sale. You want to buy a pair of jeans originally marked $32.99. What is the sale price

Oliga [24]

Answer:

Discount= $4.94

Final Price= $28.04

Step-by-step explanation:

Discount = original price x discount / 100

Discount= 32.99 x 15/ 100

Discount= 494.85/ 100

You save= $4.9485 ($494)

Final Price= original price - discount

Final Price= 32.99 - 4.9485

Final Price= $28.04

6 0

3 years ago