Respuesta :
In the right-angle triangle ABC, [tex]\angle A = 61.93^\circ[/tex], [tex]\angle C = 28.07^\circ[/tex] and AC = 34.04 units.
What is a right-angle triangle?
A right-angle triangle is a triangle in which one of its angle is right angle i. e. 90 degrees.
Given that in triangle ABC, [tex]\angle B = 90^\circ[/tex] and [tex]cos (C) = \dfrac {15}{17}[/tex].
Part A:
The angle C can be calculated as given below.
[tex]\angle C = cos^{-1} \dfrac {15}{17}[/tex]
[tex]\angle C = 28.07^\circ[/tex]
Part B:
We know that, in a triangle, the sum of all angles is equal to 180 degrees.
[tex]\angle A + \angle B +\angle C = 180^\circ[/tex]
[tex]\angle A = 180^\circ - 90^\circ - 28.07^\circ[/tex]
[tex]\angle A = 61.93^\circ[/tex]
Part C:
In triangle ABC, [tex]\angle B = 90^\circ[/tex] and [tex]\angle C= 28.07^\circ[/tex], then, AB is the perpendicular and AC is the hypotenuse.
[tex]sin 28.07^\circ = \dfrac { AB}{AC}[/tex]
[tex]0.470 = \dfrac { 16}{AC}[/tex]
[tex]AC = 34.04[/tex]
Hence we can conclude that in the right-angle triangle ABC, [tex]\angle A = 61.93^\circ[/tex], [tex]\angle C = 28.07^\circ[/tex] and AC = 34.04 units.
To know more about the right-angle triangle, follow the link given below.
https://brainly.com/question/14796244.
