Question

1.)Which inverse trigonometric function will determine the measure of angle A?

a. sin-1(5.46)
b. tan-1(0.98)
c. sin-1(1.02)
d. cos-1(0.18)

2.Find the value of sinY
a. 16/65
b. 63/65
c. 65/67
d. 67/65

Answer 1

D, B

Explanation:

Remember SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

In the first triangle, for angle A, 11 is the adjacent leg, 60 is the opposite leg, and 61 is the hypotenuse. Therefore:

sin A = 60/61 = 0.98

cos A = 11/61 = 0.18

tan A = 60/11 = 5.45

So the correct answer is D.

In the second triangle, for angle Y, 16 is the adjacent leg and 65 is the hypotenuse. To find the sine, we need to know the opposite leg. So first, use Pythagorean theorem to find the opposite leg.

c² = a² + b²

65² = 16² + b²

4225 = 256 + b²

b² = 3969

b = 63

So the sine of Y is:

sin Y = 63 / 65

Answer B.

Answer 2

1. From the given right angle triangle, the adjacent side of angle A is 11 units.

The hypotenuse is 61 units.

We use the cosine ratio to get:

`\cos(A) = (adjacent)/(hypotenuse)`

We substitute to obtain;

`\cos(A) = (11)/(61)`

`\cos(A) = 0.18`

`A=\cos^( - 1) (0.18)`

The correct choice is D.

2. From the given right triangle,

`XZ^2 + {16}^(2) = {65}^(2)`

`XZ^2 + 256 =4225`

`XZ^2 =4225 - 256`

`XZ^2 =3969`

Take positive square root

`XZ=√(3969)`

`XZ=63`

`\sin(Y) = (opposite)/(hypotenuse)`

`\sin(Y) = (63)/(65)`

The correct answer is B