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AC = <br> Round your answer to the nearest hundredth.

dusya [7]

Answer:

AC ≈ 5.03

Step-by-step explanation:

We can solve the problem above using the trigonometric ratio, they are;

SOH CAH TOA

sin Ф = opposite / hypotenuse

cosФ= adjacent/ hypotenuse

tan Ф = opposite / adjacent

From the diagram above, in reference to angle B;

opposite =AC and adjacent =BC

Since we have opposite and adjacent, the best formula to use is

tanФ = opposite / adjacent

tan B = AC / BC

tan 40 = AC/ 6

Multiply both-side of the equation by 6

6× tan 40 = AC/ 6 × 6

At the right-hand side of the equation, 6 will cancel-out 6 leaving us with just AC

6×tan 40 = AC

5.034598 = AC

AC ≈ 5.03 to the nearest hundredths

4 0

3 years ago

4.) What is the exact value of sinθ when θ lies in Quadrant II and cosθ=−513

dimaraw [331]

Answer:

Part 4) $sin(\theta)=\frac{12}{13}$

Part 10) The angle of elevation is $40.36\°$

Part 11) The angle of depression is $78.61\°$

Part 12) $arcsin(0.5)=30\°$ or $arcsin(0.5)=150\°$

Part 13) $-45\°$ or $225\°$

Step-by-step explanation:

Part 4) we have that

$cos(\theta)=-\frac{5}{13}$

The angle theta lies in Quadrant II

so

The sine of angle theta is positive

Remember that

$sin^{2}(\theta)+ cos^{2}(\theta)=1$

substitute the given value

$sin^{2}(\theta)+(-\frac{5}{13})^{2}=1$

$sin^{2}(\theta)+(\frac{25}{169})=1$

$sin^{2}(\theta)=1-(\frac{25}{169})$

$sin^{2}(\theta)=(\frac{144}{169})$

$sin(\theta)=\frac{12}{13}$

Part 10)

Let

$\theta$ ----> angle of elevation

we know that

$tan(\theta)=\frac{85}{100}$ ----> opposite side angle theta divided by adjacent side angle theta

$\theta=arctan(\frac{85}{100})=40.36\°$

Part 11)

Let

$\theta$ ----> angle of depression

we know that

$sin(\theta)=\frac{5,389-2,405}{3,044}$ ----> opposite side angle theta divided by hypotenuse

$sin(\theta)=\frac{2,984}{3,044}$

$\theta=arcsin(\frac{2,984}{3,044})=78.61\°$

Part 12) What is the exact value of arcsin(0.5)?

Remember that

$sin(30\°)=0.5$

therefore

$arcsin(0.5)$ -----> has two solutions

$arcsin(0.5)=30\°$ ----> I Quadrant

or

$arcsin(0.5)=180\°-30\°=150\°$ ----> II Quadrant

Part 13) What is the exact value of $arcsin(-\frac{\sqrt{2}}{2})$

The sine is negative

so

The angle lies in Quadrant III or Quadrant IV

Remember that

$sin(45\°)=\frac{\sqrt{2}}{2}$

therefore

$arcsin(-\frac{\sqrt{2}}{2})$ ----> has two solutions

$arcsin(-\frac{\sqrt{2}}{2})=-45\°$ ----> IV Quadrant

or

$arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\°$ ----> III Quadrant

5 0

3 years ago

Explain the purposes of inductive and deductive reasoning in mathematics. Be sure to define both inductive reasoning and deducti

uysha [10]

When it comes to deductive reasoning, it is used to reach a logical solution. You start out with the general statement, or hypothesis, and examine all the possibilities so you can reach the final conclusion.
Inductive reasoning is completely opposite - you focus on specific observations, and then make broad generalizations.

7 0

3 years ago

If a positive integer that is not a multiple of 5 is divided by 5, what is the least possible remainder

solniwko [45]

I would say 1 would be the least possible remainder...

11/5 = 2 remainder 1
21/5 = 4 remainder 1
31/5 = 3 remainder 1

and since ur dealing with positive integers (whole numbers), 1 is gonna be the smallest

8 0

3 years ago

Help me please been stuck for an hour

rewona [7]

Answer:

29/28

Step-by-step explanation:

$- \frac{2}{7} \times ( - 3 \frac{5}{8} ) \\ - \frac{2}{7} \times ( - \frac{29}{8} ) \\$

$= \frac{29}{28}$

4 0

3 years ago