The diagram shows a square with the length of the side is 12 cm. It is given that TR = 10 cm and sin x = (3)/(5) . Find the value of tan y.

Question

The diagram shows a square with the length of the side is 12 cm. It is given that TR = 10 cm and sin x =
`(3)/(5)` . Find the value of tan y.

Answer 1

tan y = 2/3

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.