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kramer
3 years ago
7

Solve the right triangle ABC with right angle C if B=30 degrees and c=10.

Mathematics
2 answers:
garri49 [273]3 years ago
4 0
<span>aâ‰8.6602, b=5, A=60 degrees Let's calculate the lengths of the sides and angles and see what option fits. Since the sum of the angles in a triangle equals 180 and we known 2 of the angles, let's calculate angle A first. A = 180 - 90 - 30 = 60 Now for side b. This is a 30/60/90 triangle. The side opposite B is half the length of c since if you were to reflect the triangle across side a, you would have an equilateral triangle. So b is 10/2 = 5. And finally, since we have a right triangle, we can use the Pythagorean theorem to get the remaining side a. So a = sqrt(10^2 - 5^2) = sqrt(100 - 25) = sqrt(75) = 5*sqrt(3) ≠8.660254038 And of the available choices, only the last one matches which is aâ‰8.6602, b=5, A=60 degrees As a side note, the last option comes close, but isn't entirely correct since the properly rounded value for a should be 8.6603, not 8.6602.</span>
kenny6666 [7]3 years ago
3 0
C=10, C=90°, B=30°, A+B+C=180°
A+30°+90°=180°⇒A=60°

cos30°=a/c
cos30°=a/10⇒a=cos30°*10
a<span>≃8.6602


c²=a²+b²⇒b²=c²-a²
b²=10²-8.6602²⇒b²=25
b=5
</span>
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The answer is the graph b.
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2 years ago
Which biconditional is not a good definition?
Xelga [282]
<span>The <u>correct answers</u> are:

A ray is a bisector of an angle if and only if it splits the angle into two angles; and
A) I can afford to buy a ticket.

Explanation<span>:

For the first question, the first three answers are very specific and true:

A whole number is odd if it is not divisible by 2, and a number is not divisible by 2 if it is odd;
an angle is straight if its measure is 180 degrees, and the measure of an angle is 180 degrees if it is a straight angle;
a whole number is even if it is divisible by 2, and a number is divisible by 2 if it is even.

However, with the fourth choice, we are missing a key word in the definition. A ray is a bisector of an angle if and only if it splits the angle into two <u>CONGRUENT</u> angles. It is not just a ray that cuts an angle into two pieces, the pieces must be equal.

For the second question, the Law of Detachment says if our conditional "if p, then q" is true and p is true, then q must also be true.

For this question, "I can go to the concert if I can afford to buy a ticket" is true as well as "I can go to the concert." This means "I can afford to buy a ticket" must be true as well.</span></span>
4 0
3 years ago
You place the spring vertically with one end on the floor. You then drop a book of mass 1.50 kg onto it from a height of 0.900 m
Alex777 [14]

Answer:

The value of the maximum distance the spring will be compressed  

x = 0.143 m= 14.3 cm

Step-by-step explanation:

Given data

Mass m = 1.5 kg

h = 0.9 m

k = 1500\frac{N}{m}

Since the book is released from a height h = 0.9 m above the top of the spring. so the total distance

y = h + x

Now in that case for the spring

mg y= \frac{1}{2} k x^{2}

mg(h +x) = \frac{1}{2} k x^{2}

By rearranging the above equation we get

k x^{2}  - 2mgx - 2mg h = 0

Put all the values in above equation we get

1500x^{2}  - 29.43 x - 26.48 = 0

By solving the above equation we get

x = 0.143 m= 14.3 cm

This is the value of the maximum distance the spring will be compressed.

8 0
2 years ago
Log 3 x=4 pls and thx
Fantom [35]

Answer:

D

Step-by-step explanation:

Using the law of logarithms

• log_{b} x = n ⇔ x = b^{n}

given

log_{3} x = 4 ⇒ x = 3^{4} = 81 → D

8 0
2 years ago
the straight line L, has equation y=3x-4 The straight line 1, in perpendicular to L, and passes through the point (9.5) Find an
kari74 [83]

Given:

The equation of given line is

y=3x-4

A line is perpendicular to the given line and passes through the point (9,5).

To find:

The equation of the perpendicular line.

Solution:

We have,

y=3x-4

On comparing this equation with slope intercept form y=mx+b, we get

m=3

It means, the slope of the given line is 3.

The product of slopes of two perpendicular lines is -1.

m\times m_1=-1

3\times m_1=-1

m_1=-\dfrac{1}{3}

Point slope form of a line is

y-y_1=m(x-x_1)

Where, m is the slope.

The slope of perpendicular line is -\dfrac{1}{3} and it passes through the point (9,5). So the equation of the line is

y-5=-\dfrac{1}{3}(x-9)

y-5=-\dfrac{1}{3}(x)-\dfrac{1}{3}(-9)

y-5=-\dfrac{1}{3}x+3

Adding 5 on both sides, we get

y-5+5=-\dfrac{1}{3}x+3+5

y=-\dfrac{1}{3}x+8

Therefore, the equation of required line is y=-\dfrac{1}{3}x+8.

5 0
2 years ago
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