Question

Match the trigonometric ratios with their values based on the triangle shown in the diagram.

Answer 1

Answer:

sin D = 4/5

sin C = 3/5

sin D x cos D = 12/25

cos C x tan D = 16/15

Step-by-step explanation:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

then

sin D = 4/5

sin C = 3/5

sin D x cos D = 4/5 x 3/5 = 12/25

cos C x tan D = 4/5 * 4/3 = 16/15

Answer 2

Sin D - 4/5
This is because sin would mean Opposite/Hypotenuse, and so if the angle is D then the opposite is 4.

sin C - 3/5
This is basically the same reason as sin D, however this time the Opposite is 3.

sin D × cos D - 4/5 × 3/5 = 12/25
For here, you just get the fractions of sin D, which we got earlier, and cos D, which would be Adjacent/Hypotenuse and therefore 3/5.

tan C × tan D - Not an option

cos C × tan D - 16/15
This is because cos C would be 4/5, and tan D would be 4/3 (Opposite/Adjacent) and multiplying those fractions together gives 16/15.

I hope this helps!