Respuesta :
Answer:
The option which is the closest to the measure of ∠A is 74°
Step-by-step explanation:
The question is answered using the options provided by a similar question from an online source
When tan A = (7/2), we have;
The trigonometric ratio for the tangent of an angle is given as follows;
[tex]tan\angle A = \dfrac{Opposite \ leg \ length}{Adjacent \ Leg \ length} = \dfrac{sin \angle X}{cos\angle X}[/tex]
tan A = (7/2) = 3.5
sin(30°) = 1/2, cos(30°) = (√3/2)
sin(60°) = (√3/2), cos(60°) = (1/2)
sin(45°) = cos(45°) = (√2/2)
tan(30°) = (1/2)/(√3/2) = (√3)/3
tan(45°) = 1
tan(60°) = (√3/2)/(1/2) = √3
The tangent of an angle is increasing as we move from 0° to 90°
Therefore, given that tan A = 7/2 > tan 60° = √3, we have;
∠A > 60°
The option (the options obtained from an online source are; 15°, 39°, 58°, and 74°) which is the closest to the measure of ∠A is 74°.
