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3 years ago

Calculate the length b to two decimal places.

Mathematics

1 answer:

Andrej [43]3 years ago

6 0

Answer:

B. 21.64

Step-by-step explanation:

We have been given a triangle and we are asked to find the length of AC (b).

We will use law of cosines to find the length of side AC.

$c^{2}=a^{2}+b^{2}-2ab \text{ cos }\theta$

Upon substituting our given values in the formula we will get,

$(AC)^{2}=15^{2}+12^{2}-2\times 15\times 12 \text{ cos}(106)$

$(AC)^{2}=225+144-360\text{ cos}(106)$

$(AC)^{2}=369-360(-0.275637355817)$

$(AC)^{2}=369+99.22944809412$

$(AC)^{2}=468.22944809412$

Upon taking square root of both sides of our equation we will be get,

$AC=\sqrt{468.22944809412}$

$AC=21.6386101238993629\approx 21.64$

Therefore, the length of b is 21.64 and option B is the correct choice.

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3 years ago

Fill in the gaps in this sequence: -8, -19, -30, _ , _.<br> (Geometric and arithmetic sequences)

gavmur [86]

-8, -19, -30, -49 , -60

<u>Step-by-step explanation:</u>

Here we have the following sequence :

-8, -19, -30, _ , _

First term of sequence is -8 .
Second term of sequence is -19 : $-8-11 = -19$
Third term of sequence is -30 : $-19-11 = -30$
Fourth term of sequence is : $-30-11 = -49$
Fifth term of sequence is : $-49-11 = -60$

Following sequence was an AP( Arithmetic Progression ) with first term as -8 i.e. $a = -8$ and common difference $d = -11$ having general equation as : $-8 -11n$ .