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julia-pushkina [17]
3 years ago
5

If x is a positive acute angle and cos x = 3/5, find the value of sinx.

Mathematics
1 answer:
Dima020 [189]3 years ago
3 0
X is a positive acute angle. That means x is located in the first quadrant and has positive value in sin, cos, tan.

The formula of trigonometry ratio
cos x = \dfrac{\text{adjacent}}{\text{hypotenuse}}
sin x = \dfrac{\text{opposite}}{\text{hypotenuse}}

From the formula of cosine
cos x = \dfrac{3}{5}
\dfrac{\text{adjacent}}{\text{hypotenuse}}= \dfrac{3}{5}
from the formula above, adjacent side is 3 units, and hypotenuse is 5 units

Draw a right triangle to illustrate the location of the sides. See image attached.

To find the ratio of sine, we need to find the length of opposite side using pythagorean theorem
3² + (opposite)² = 5²
9 + (opposite)² = 25
(opposite)² = 25 - 9
(opposite)² = 16
opposite = 4
The length of opposite side is 4 units

Find sin x
sin x = \dfrac{\text{opposite}}{\text{hypotenuse}}
sin x = \dfrac{4}{5}

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MrMuchimi

Answer:

  y = 5/3x +5

Step-by-step explanation:

The two-point form of the equation of a line is useful here.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (0 -(-5))/(-3 -(-6))(x -(-6)) -5

  y = 5/3(x +6) -5

  y = 5/3x +5 . . . . slope-intercept form

  5x -3y = -15 . . . .standard form

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3 years ago
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At a restaurant you meal is $20. In addition to the cost of the meal you must pay a 5% sales tax and leave a 15% tip. What is th
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7 0
3 years ago
PQ and QR are two sides of a regular 12-sided polygon. PR is the diagonal of the polygon.
skelet666 [1.2K]

The size of angle PRQ is 15°

Step-by-step explanation:

In any regular polygon of n-sided

  • All sides are equal in length
  • All angles are equal in measure
  • The measure of each interior angle is \frac{(n-2)*180}{n}
  • The measure of each exterior angle is \frac{360}{n}
  • The sum of the measures of the interior and exterior angle at the same vertex is 180°

∵ PQ and QR are two sides of a regular 12-sided polygon

∴ PQ = QR

∵ PR is a diagonal

∴ ∠PQR is an interior angle of the polygon

- By using the rule of the interior angle above

∵ n = 12

∴ m∠PQR = \frac{(12-2)*180}{12}

∴ m∠PQR = 150°

In Δ PQR

∵ PQ = QR ⇒ sides in a regular polygon

- Δ PQR is an isosceles Δ

∴ m∠PRQ = m∠RPQ ⇒ base angles of an isosceles Δ

The sum of the measures of the interior angles of a triangle is 180°

∵ m∠PQR + m∠PRQ + m∠RPQ = 180°

∴ 150 + m∠PRQ + m∠RPQ = 180°

- Subtract 150 from both sides

∴ m∠PRQ + m∠RPQ = 30

∵ m∠PRQ = m∠RPQ

- Divide their sum by 2 to find the measure of each one

∴ m∠PRQ = m∠RPQ = 30 ÷ 2 = 15°

∴ m∠PRQ = 15°

The size of angle PRQ is 15°

Learn more:

You can learn more about the triangles in brainly.com/question/3945600

#LearnwithBrainly

4 0
3 years ago
Given the equation 4X +7 = 3 (2x -5 ) solve for the variable explain each step in justify your process
alexandr1967 [171]

Answer:

x = 11

Step-by-step explanation:

4x + 7 = 6x -15

4x - 6x = -15-7

-2x = -22 / : (-2)

x = 11

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below :)

5 0
3 years ago
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