In triangle JKL, tan(b°) = 3/4 and sin(b°)= 3/5 if triangle JKL is dilated by a scale factor of 3 what is cos(b°)

If triangle JKL is dilated with a scale factor of 3, cos (b°) = =

Step-by-step explanation:

Step 1; In the triangle JKL, we have tan (b°) = and sin (b°) = . The tan of any angle can be calculated by dividing the opposite sides length by the adjacent sides length while the sine of any angle can be calculated by dividing the opposite side by the hypotenuse. So,

tan (b°) = = , so opposite side = 3, adjacent side = 4.

sin (b°) = = , so opposite side = 3, hypotenuse = 5.

Since both the angles have the same lengths of the opposite sides, the adjacent sides and the hypotenuse are both in the same ratios. So for the triangle JKL, opposite sides length = 3, adjacent sides length = 4, hypotenuse = 5.

Step 2; If the triangle is dilated by a scale factor of 3, the entire triangle is 3 times larger than the original size so all the sides are also 3 times larger than they used to be. So,

opposite side = 3 × 3 = 9,

Adjacent side = 4 × 3 =12,

Hypotenuse = 5 × 3 = 15.

The cosine of any angle is given by dividing the adjacent sides length by the hypotenuses length. Using the calculated lengths,

cos(b°) = = = .

answer is because 4×10=40

and 98×4= is 392

40,392