Question

Can someone help me plz .. Use these lengths to find cos B, tan B, and sin B.

Answer 1

cos B =
`(7)/(25)`

tan B =
`(24)/(7)`

sin B =
`(24)/(25)`

Explanation:

In the right triangle, there are three sides and 2 acute angles

• Hypotenuse ⇒ the opposite side of the right angle

• Leg1 and Leg 2 ⇒ the sides of the right angle

The trigonometry functions of one of the acute angles Ф are

• sin Ф = opposite leg/hypotenuse

• cos Ф = adjacent leg/hypotenuse

• tan Ф = opposite leg/adjacent leg

In Δ ACB

∵ ∠C is the right angle

∴ AB is the hypotenuse

∵ AC is the opposite side of ∠B ⇒ leg1

∵ CB is the adjacent side of ∠B ⇒ leg2

→ By using the ratios above

∴ cos B =
`(CB)/(AB)` , tan B =
`(AC)/(CB)` , sin B =
`(AC)/(AB)`

∵ CB = 7, AB = 25, AC = 24

∴ cos B =
`(7)/(25)`

∴ tan B =
`(24)/(7)`

∴ sin B =
`(24)/(25)`