Please Help Me!<br> The product of a number and -(1/2) is the same as 49. Find the number

zhenek [66]

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the ∠BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

$sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
$tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ ABC

∵ ∠ BCA is a right angle

∴ The hypotenuse is AB

∵ The adjacent side to ∠CAB is AC

∵ The opposite side to ∠CAB is BC

∵ AB = 13 units ⇒ hypotenuse

∵ CB = 12 units ⇒ opposite

∵ AC = 5 units ⇒ adjacent

- Let us find the trigonometry ratios of angle BAC

∵ m∠CAB is x

∵ $sin(x)=\frac{BC}{AB}$

∴ $sin(x)=\frac{12}{13}$

∴ $x=sin^{-1}(\frac{12}{13})$

∵ $cos(x)=\frac{AC}{AB}$

∴ $cos(x)=\frac{5}{13}$

∴ $x=cos^{-1}(\frac{5}{13})$

∵ $tan(x)=\frac{BC}{AC}$

∴ $tan(x)=\frac{12}{5}$

∴ $x=tan^{-1}(\frac{12}{5})$

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

#LearnwithBrainly

4 0

3 years ago

Read 2 more answers

Please help me on 7 and 8

Nostrana [21]

What are the questions on 7 and 8?

3 0

3 years ago

Julia swam 3/4 of a mile in the pool.if each lap is 1/16 of a mile,how many laps did she swim.

lions [1.4K]

The answer is twelve because to Make the two fractions denominators equal you have to multiply the numerator and denominator by 4 to get the denominators equal which gets you a fraction of 12/16 and if you divide that by 1/16 because that is how long each lap is then you get 16 which is the amount of laps they swam

5 0

4 years ago

Read 2 more answers

Kate made a box to hold her jewelry collection. She used 42 inches of wood to build the sides of the box. If the box was 9 Inche

Vladimir [108]

Assuming that the sides of the box are square (having 90° angles on all four corners), then it should be relatively easy for us to find the length of the box, given the perimeter and the length of one side.
We know the length of all sides combined is 42 inches, and that the length of one side is 9 inches. With a rectangular prism, the length of one side is the same as the length of the opposite side, so there are two sides that measure 9 inches.
All we need to do to find the measure of both the other sides' lengths is subtract the known lengths from the total length.

9 + 9 = 18

42 - 18 = 24

So the rest of the side lengths added together is 24 inches.
There are two sides left, so all we have to do is divide by 2 to find the length of the box.

24 / 2 = 12

The length of Kate's jewelry box is 12 inches.
Hope that helped =)

3 0

3 years ago

The area of a rectangle is 24 square inches. Determine both dimensions if the length is 6 inches less than three times the width

Rama09 [41]

Answer:

width is 4 inches

length is 6 inches

Step-by-step explanation:

the length is 6 inches less than three times the width

l = 3w - 6

a = l * w

a = (3w - 6)w

a = 3w^2 - 6w

area of the rectangle is 24 square inches

3w^2 - 6w = 24

subtract 24 from both sides

3w^2 - 6w - 24 = 0

Divide both sides by 3

w^2 - 2w - 8 = 0

Factor

(w - 4)(w + 2) = 0

w = {-2, 4}

disregard the negative root since measurement must be positive

w = 4

l = 3w - 6

l = 3(4) - 6

l = 6

3 0

3 years ago

Please Help Me! The product of a number and -(1/2) is the same as 49. Find the number