In triangle JKL, sin(b°) = three fifths and cos(b°) = four fifths. If triangle JKL is dilated by a scale factor of 2, what is ta

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).