Question

41) In right triangle ABC, AC = 9 and BC = 12 The sine of angle y is

Answer 1

Let's put more details in the given figure to understand the problem:

From the figure above, we have three (3) named angles: ∠x, ∠y & ∠z

Using the principle of trigonometric functions, we get:

`\text{ Sin y = Cos x}`

With the given AC = 9 and BC = 12, we can find ∠x using the Tangent Function. We get,

`\text{ Tan x = }\frac{\text{ 9}}{\text{ 12}}`
`\text{ x = }\tan ^(-1)\text{ (}(9)/(12))`

`\text{ x = 36.8698976}^(\circ)\text{ }\approx36.87^(\circ)`

Let's now determine what is Cos x.

`\text{ Cos x = Cos (36.87}^(\circ))`

`\text{ Cos x = 0.7999989 }\approx\text{ 0.8}`

Since Cos x = Sin y, therefore, we can conclude that Sin y = 0.8

ANSWER: Letter B - 0.8