Answer:
Therefore Based on the Figure only the third option i.e C. ic True
[tex]\cos 28\° = \dfrac{17}{c}[/tex]
Step-by-step explanation:
Given:
Let label the figure first such that
In Δ ABC , ∠C = 90° , ∠ B = 62°,
[tex]\sin 62\°=\dfrac{17}{c}[/tex]
AB = Hypotenuse = c
AC = 17
To Find:
True Statements
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180[/tex]
Substituting the values we get
[tex]\angle A +62+90=180\\\angle A=180-152=28\\\angle A=28\°[/tex]
In Right Angle Triangle ABC , Cosine Identity we have
[tex]\cos A = \dfrac{\textrm{side adjacent to angle A}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\cos 28\° = \dfrac{AC}{AB}=\dfrac{17}{c}\\\\\cos 28\°=\dfrac{17}{c}[/tex]
Here in this figure
[tex]\tan B = \dfrac{\textrm{side opposite to angle B}}{\textrm{side adjacent to angle B}}[/tex]
[tex]\sin A = \dfrac{\textrm{side opposite to angle A}}{Hypotenuse}\\[/tex]
Substituting we get
[tex]\tan 62\° = \dfrac{17}{BC}[/tex]
[tex]\cos 62\° = \dfrac{BC}{c}[/tex]
[tex]\sin 28\° = \dfrac{BC}{c}[/tex]
Therefore Based on the Figure only the third option i.e C. is True
[tex]\cos 28\° = \dfrac{17}{c}[/tex]
