Question

from the adjoining figure, find (1) sin x , (2) cos y​

Answer 1

Solution:

To calculate sin(x) and cos(y), we have to calculate the sides BD and AD.

In ∆BCD, we have:

→ BD = ?

→ BC = 4 unit.

→ CD = 3 unit.

Applying Pythagoras Theorem On ∆BCD:

→ BD² = BC² + CD²

→ BD² = 4² + 3²

→ BD² = 16 + 9

→ BD² = 25

→ BD = √25

→ BD = 5 unit. ★

In ∆ABD, we have:

→ AB = 12 unit.

→ BD = 5 unit.

→ AD = ??

Applying Pythagoras Theorem on ∆ABD:

→ AD² = AB² + BD²

→ AD² = 12² + 5²

→ AD² = 144 + 25

→ AD² = 169

→ AD = √169

→ AD = 13 unit. ★

Now, lets calculate the values of sin(x) and cos(y)

We have:

→ sin(x) = Perpendicular / Hypotenuse

With respect to angle x:

→ Perpendicular = BC

→ Hypotenuse = BD

Therefore:

→ sin(x) = BC / BD

→ sin(x) = 4 / 5 ★

We have:

→ cos(y) = Base / Hypotenuse

With respect to angle y:

→ Base = AB

→ Hypotenuse = AD

Therefore:

→ cos(y) = 12 / 13 ★

Answer:

• sin(x) = 4/5
• cos(y) = 12/13