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2 years ago

Use the Law of Sines to find the missing angle of the triangle. Find m<b to the nearest tenth.

Mathematics

1 answer:

defon2 years ago

6 0

1. By the Law of Sines, you have:

SinA/a=SinB/b=SinC/c

2. You don't need the fraction SinC/c, so you can eliminate it. Then:

SinA/a=SinB/b

A=40°
a=19
B=m∠b
b=13

3. When you substitute this values into SinA/a=SinB/b, you obtain:

SinA/a=SinB/b
Sin(40°)/19=SinB/13
SinB=13xSin(40°)/19
m∠b=SinB^-1(13xSin(40°)/19)
m∠b=26.1°

Therefore, the answer is: 26.1 degrees.

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2 years ago

Which of the following points are more than 5 units from the point P(−2, −2)? Select all that apply. A A (2, 1) B B (4, −1) C C

netineya [11]

The distance between any 2 points P(a,b) and Q(c,d) in the coordinate plane, is given by the formula:

 $|PQ|= \sqrt{ (a-c)^{2} + (b-d)^{2}}$

Using this formula we calculate the distances |PA|, |PB|, |PC|, |PD| and |PE| and compare to 5.

$|PA|= \sqrt{ (-2-2)^{2} + (-2-1)^{2}}= \sqrt{16+9}= \sqrt{25}=5$

$|PB|= \sqrt{ (-2-4)^{2} + (-2+1)^{2}}= \sqrt{36+1}= \sqrt{37} \approx 6$

$|PC|= \sqrt{ (-2-2)^{2} + (-2+3)^{2}}= \sqrt{16+1}= \sqrt{17}\approx4$

$|PD|= \sqrt{ (-2+6)^{2} + (-2+6)^{2}}= \sqrt{16+16}= \sqrt{32}\ \textgreater \ \sqrt{25}=5$

$|PE|= \sqrt{ (-2+5)^{2} + (-2-1)^{2}}= \sqrt{9+9}= \sqrt{16}=4$

Answer: B and D

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3 years ago

What is 76.78 rounded to the nearest whole number?

galben [10]

Lets look at the number. 76.78. In each of the different place holders the number is higher than 5. Lets do some examples. 74 rounded to the nearest whole number is going to be 70. 76 rounded to the whole number will be 80. The .78 in your question also contributes.

Answer: 80

6 0

3 years ago

Read 2 more answers

Factor 200t+83 - 80t2. A. 8t(t - 5)(t + 5) B. 8t(t - 5)2 C. -8t(t - 5)(t + 5)

Mashutka [201]

Step-by-step explanation:

8t³-80t²+200t

= 8(t³-10t+25)

= 8t(t²-10t+25)

= 8t(t-5)(t-5)

= 8t(t-5)²

the answer is B.

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2 years ago