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3 years ago

Find the length of AC on this triangle

Mathematics

1 answer:

Illusion [34]3 years ago

4 0

Answer:

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan12° = $\frac{opposite}{adjacent}$ = $\frac{AC}{BC}$ = $\frac{AC}{44}$ ( multiply both sides by 44 )

44 × tan12° = AC , then

AC ≈ 9.35 ( to 2 dec. places )

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How to solve (-9)-16 subtracting integers

Ugo [173]

-9-16 = 0-9-16 = 0-25 = -25

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=cos%20%5B%20arctan%28%5Cfrac%7B12%7D%7B5%7D%29%20-%20arcsin%20%28%5Cfrac%7B-3%7D%7B5%7D%29%5D"

qwelly [4]

Answer: -16/65

Step-by-step explanation:

Drawing the right triangle (as attached) gives us that $\arctan \left(\frac{12}{5} \right)=\arcsin \left(\frac{12}{13} \right)$

Also, $-\arcsin \left(-\frac{3}{5} \right)=\arcsin \left(\frac{3}{5} \right)$

This means our original expression is equal to:

$\cos \left[\arcsin \left(\frac{12}{13} \right)+\arcsin \left(\frac{3}{5} \right) \right]$

Using the cosine addition formula, which states $\cos(a+b)=\cos a \cos b-\sin a \sin b$ , we get this itself is equal to:

$\cos \left(\arcsin \left(\frac{12}{13} \right) \right)\cos \left(\arcsin \left(\frac{3}{5} \right)\right)-\sin \left(\arcsin \left(\frac{12}{13} \right) \right)\sin \left(\arcsin \left(\frac{3}{5} \right)\right)$

Since $\sin^{2} \theta+\cos^{2} \theta=1$ , we know that:

$\sin^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)+\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\\frac{144}{169} +\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{25}{169}\\\\cos \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{5}{13}$

Similarly, cos(arcsin(3/5))=4/5.

This means the given expression is equal to:

$\left(\frac{5}{13} \right) \left(\frac{4}{5} \right)-\left(\frac{12}{13} \right) \left(\frac{3}{5} \right)\\\\\frac{20}{65}-\frac{36}{65}=\boxed{-\frac{16}{65}}$

3 0

2 years ago

On each of three pieces of paper a three digit number is written two of the digits are covered . The sum is 826. What is the sum

Ket [755]

Answer:

Step-by-step explanation:

The diagram showing the three pieces of paper of three digit in which two of the letters were covered can be seen below.

From the diagram; we have;

243 , 1_7 , _26

Assuming the covered digits are _

The sum is 826.

i.e

243 + 1_7 + _26 = 826

The objective is to determine the sum of the two unknown digits

So; we need to think about what number can we add put in 1_7 to determine the covered digit in _26

From ; 1_7 , we have the choice to pick from 0 - 9

Assuming the covered digit is 0; let's check if we are right

So; 243 + 107 + _26 = 826

350 + _26 = 826

_26 = 826 - 350

_26 = 476

So; the covered digit is in the position of 4 , but it doesn't tally together

i.e 426 is not the same as 476, which makes our assumption to be wrong.

Let consider the covered digit to be 5 for example.

So; 243 + 157 + _26 = 826

400 + _26 = 826

_26 = 826 - 400

_26 = 426

The covered digit is in the position of 4

SO;

426 = 426

Here , our assumption is right.

As such , the covered digits are 5 and 4

The sum of the two covered digits are = 5 + 4 = 9

7 0

3 years ago

2/5 x = 3 1/5 ASAP ill give brainliest

yKpoI14uk [10]

Answer:

15 1/2

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

7 pencils cost £5.95. How much do 11 pencils cost?

yuradex [85]

Answer:

11 pencils cost £9.35.

Step-by-step explanation:

Given;

7 pencils = £5.95

1 pencil = 5.95 ÷ 7

= £0.85

Now,

11 pencils = 11 × 0.85

= £9.35

5 0

3 years ago

Read 2 more answers