Answer:
1.6 m
Step-by-step explanation:
The side of the sign, the ground, and the wire form a right triangle where the wire is the hypotenuse.
The angle of depression plus the upper interior angle of the triangle add to 90 degrees. That means that the upper acute angle of the triangle measures 90 - 28 = 62 deg.
Call the upper acute angle of the triangle Angle A and the height of the sign h.
tan A = opp/adj
tan 62 = 3/h
h tan 62 = 3
h = 3/tan 62
h = 1.6
Answer: 1.6 m
Answer:
The tall of the sign board is 1.6 m.
Step-by-step explanation:
Let's draw a diagram to represents the given situation.
In the diagram, the base of the festival sign to the ground forms 90°. So it is right triangle.
The angle of depression is 28°. The angle of the upper interior angle = 90° - 28° = 62°.
Now we can use the trigonometric ration "tan = [tex]\frac{Oppsoite}{Adjacent}[/tex]" and the height of the sign board.
Let's take "h" be the height/tall of the sign board.
As you can see in the diagram, the opposite side = 3m
Now plug in the given values in the tan ratio, we get
tan 62° = [tex]\frac{3}{h}[/tex]
The value of tan 62° = 1.88
So, 1.88 = [tex]\frac{3}{h}[/tex]
h = [tex]\frac{3}{1.88}[/tex]
h = 1.595
We are asked to round of the nearest tenths place.
So, h = 1.6 m
Therefore, the tall of the sign board is 1.6 m.
