Answer:
Tan(b°) = 3/4, which is equivalent to three fourths (C).
Step-by-step explanation:
Triangle JKL is a right triangle with angle K being the right angle and angle L equal to b°.
We will employ SOHCAHTOA principles from trigonometry to calculate the sides' values.
For triangle ∆JKL:
Sin(b°) = opposite/hypotenuse
Sin(b°) = 3/5
Cos(b°) = adjacent/hypotenuse
Cos(b°) = 4/5
Tan(b°) = 3/4.
From the earlier information, we have the values for each side of triangle ∆JKL.
Please refer to the attached diagram for the triangle (1).
Triangle ∆JKL is scaled with a factor of 2.
This implies multiplying each side of ∆JKL by 2, resulting in:
Opposite side = 2(3) = 6
Adjacent side = 2(4) = 8
Hypotenuse = 2(5) = 10.
To find tan(b°) for the new triangle, we use the tangent ratio:
Tan(b°) = opposite/adjacent.
Tan(b°) = 6/8.
Tan(b°) = 3/4.
Find the diagram for the new triangle included (2).
Diagram 3 provides a depiction of both triangles.
As shown, the angle remains unchanged when a triangle is scaled by a factor.
Thus, we conclude that tan(b°) = three fourths (C).
