Question

From the given figure, the value of cos y is:

Options

• `1/3`

• `1/4`

• `12/13`

• `1 1/12`

Answer 1

`bb(12/13)`

Explanation:

In the right-angled triangle on the right with legs of lengths 3 cm and 4 cm, the hypotenuse is:

\[\sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\text{ cm}\]

This shared vertical side acts as the perpendicular (height) of the left-hand right-angled triangle, which has a base of 12 cm. Using the Pythagorean theorem, the hypotenuse of the left triangle is:

\[\sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13\text{ cm}\]

For the angle y, the cosine is the ratio of the base to the hypotenuse:

\[\cos y = \frac{\text{Base}}{\text{Hypotenuse}} = \frac{12}{13}\]