episodediamond13
contestada

question 1. Enter the ratio equivalent to sin(B)

question 2. Consider this a right triangle. enter the measure of angle CAB to the nearest hundredth degree.

question 3. Suppose angle A is an angle such that angle cosA < sinA. select ALL angle measures that are possible values for angle A. 25, 35, 45, 55, 66, 75.

question 1 Enter the ratio equivalent to sinB question 2 Consider this a right triangle enter the measure of angle CAB to the nearest hundredth degreequestion 3 class=
question 1 Enter the ratio equivalent to sinB question 2 Consider this a right triangle enter the measure of angle CAB to the nearest hundredth degreequestion 3 class=

Respuesta :

Answer:

The three questions about the given triangle has been answered below.

Step-by-step explanation:

We are given a right angled triangle whose sides are of length 20, 21 and 29.

(1) sin(B) = [tex]\frac{side opposite to B}{hypotenuse}[/tex]

              = [tex]\frac{21}{29}[/tex]

              = 0.72

(2) sin(A) = [tex]\frac{20}{29}[/tex]

     sin(A)  = 0.689

     ∠CAB = [tex]sin^{-1}(0.689)[/tex]

     ∠CAB = 43.551°

(3) We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.

From the given options the angles that satisfy this are 55 , 66 and 75.

45 is not included as then sinA = cosA and that condition is not there.

We can use sine and cosine trigonometric ratios to calculate the ratio and measures of angles.

A: The ratio equivalent to sin(B) is  [tex]\dfrac{21}{29}[/tex]

B: The measure of angle  ∠CAB is  [tex]43.6^\circ[/tex]

C: The possible measures of angle A can be: 55, 66 or 75

Given that:

  • AB = 29 units
  • BC = 20 units
  • CA = 21 units

Using definitions of specific trigonometric ratios:

A: The ratio equivalent to sin(B) is:

[tex]sin(B) = \dfrac{CA}{AB} = \dfrac{21}{29}\\[/tex]

B: The measure of angle ∠CAB is calculated as:

[tex]sin(A) = \dfrac{CB}{BA} = \dfrac{20}{29} = 0.69\\\\A = arcsin(0.69) = 43.6^{\circ}\\\\\angle CAB = 43.6^{\circ}[/tex]

C: When sin A > cos A, the measures of angle A from 25,35,45,55,66,75 are:

55, 65 and 75:

The reason for the angles possible are 55, 66 ,75 is that:

[tex]\theta \leq 45\\sin(\theta) \leq cos(\theta)[/tex]

Thus, we have:

A: The ratio equivalent to sin(B) is  [tex]\dfrac{21}{29}[/tex]

B: The measure of angle  ∠CAB is  [tex]43.6^\circ[/tex]

C: The possible measures of angle A can be: 55, 66 or 75

Learn more about trigonometric ratios here:

https://brainly.com/question/95152