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satela [25.4K]
4 years ago
6

In triangle abc, angle A is the right angle. What is the value of y?

Mathematics
2 answers:
Nesterboy [21]4 years ago
4 0

Answer:

7sinΠ/6 (A)

Step-by-step explanation:

Since the triangle given is a right angled triangle, the SOH CAH TOA method will be employed.

Given opposite side to be 'y' (the side facing the acute angle)

The hypotenuse = 7feet(the longest side)

Any the angle theta = 30°

According to SOH;

sin(theta) = opposite/Hypotenuse

Sin30° = y/7

y = 7sin30°

Note that 180°=Πrad

30° = Π/6rad

y = 7sinΠ/6 (A)

Natalka [10]4 years ago
3 0

Answer:

A

Step-by-step explanation:

In a right triangle, the side opposite to the 90 degree angle (here, side opposite to angle A) is known as the hypotenuse.

Also, the side that is "opposite" to the angle given (here side opposite is y to angle given 30 degrees) is the opposite side.

Since we want to find "opposite" and have "hypotenuse" , recalling trig ratios, we can say opposite/hypotenuse is the ratio SINE, so we can write:

Sin(30)=\frac{y}{7}

We solve for y:

Sin(30)=\frac{y}{7}\\y = 7 Sin(30)

Since the answer choice has angles in radians, we recall 30 degrees is \frac{\pi}{6} radians.

Thus, the correct answer is  7Sin(\frac{\pi}{6}), or option A

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3 years ago
If 10000 is invested at an interest rate of 10 per year ,compound semiannually,find the value of the investment after the given
slega [8]

Answer:

Part a) \$17,958.56  

Part b) \$32,251.00  

Part c) \$57,918.16

Step-by-step explanation:

<u><em>The complete question is</em></u>

If $10,000 is invested at an interest rate of 10% per year, compounded semiannually, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)

a)6 years

b)12 years

c)18 years

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part a) 6 years

we have  

t=6\ years\\ P=\$10,000\\ r=10\%=10/100=0.10\\n=2  

substitute in the formula above  

A=10,000(1+\frac{0.10}{2})^{2*6}  

A=10,000(1.05)^{12}  

A=\$17,958.56  

Part b) 12 years

we have  

t=12\ years\\ P=\$10,000\\ r=10\%=10/100=0.10\\n=2  

substitute in the formula above  

A=10,000(1+\frac{0.10}{2})^{2*12}  

A=10,000(1.05)^{24}  

A=\$32,251.00  

Part c) 18 years

we have  

t=18\ years\\ P=\$10,000\\ r=10\%=10/100=0.10\\n=2  

substitute in the formula above  

A=10,000(1+\frac{0.10}{2})^{2*18}  

A=10,000(1.05)^{36}  

A=\$57,918.16

7 0
4 years ago
Solve the triangle. A = 46°, a = 31, b = 27
Gnesinka [82]

Answer:

A=46 degrees, B=33.4 degrees, C=100.6 degrees

a=34, b=27, c=48.2

Step-by-step explanation:

(a/sin(A)) = (b/sin(B)) = (c/sin(C))

we are given

(34/sin(46)) = (27/sin(B))

34sin(B) = 26sin(46)

34sin(B) = 18.702834809

sin(B) = 0.550083377

note use inverse sin function to find angle B

B = 33.372733167 approx 33.4 degrees then

C = 180 - (46 + 33.4) = 100.6

Then, (b/sin(B)) = (c/sin(C))

27/0.550083377 = c/0.982935349

0.550083377 * c = 27 * 0.982935349

0.550083377 * c = 26.539254427

c = 48.245876056 approx 48.2 .

Lastly, you get: A=46 degrees, B=33.4 degrees, C=100.6 degrees

a=34, b=27, c=48.2

6 0
3 years ago
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