Answer:
tan y = 2/3
Step-by-step explanation:
The question is a word problem regarding trigonometric ratios
The given parameters are;
The side length of the square = 12 cm
The measure of segment TR = 10 cm
sin x = 3/5
By sine rule, given that ΔRST is a right triangle, we have;
RS = TR × sin(x)
∴ RS = 10 cm × 3/5 = 6 cm
RS = 6 cm
By Pythagoras's theorem, we have;
TS = √(TR² - RS²)
∴ TS = √((10 cm)² - (6 cm)²) = 8 cm
TS = 8 cm
By the definition of trigonometric ratios, we have;
tan (θ) of a right triangle = (Opposite leg length)/(Adjacent leg length)
∴ tan y = TS/QS
QS = A side length of the square = 12 cm
∴ tan y = (8 cm)/(12 cm) = 2/3
tan y = 2/3.
