Question

In a right triangle the cosine of an acute angle is 1/2 and the hypotenuse measures 7 inches. What is the length of the side of the triangle adjacent to this angle?

Answer 1

The length of side adjacent to the cosine angle is
`(7)/(2)` inches

Explanation:

Given as :

For a right triangle ,

Cosine of an acute angle =
`(1)/(2)`

I.e cos Ф =
`(1)/(2)`

And, The measure of hypotenuse = 7 inches

Let the length of side adjacent to the cos Ф = x inches

SO, cos Ф =
`(Base)/(Hypotenuse)`

Or, cos Ф =
`(Base)/(7)`

Or, Base = 7 × cosФ

Or, Base = 7 ×
`(1)/(2)`

∴ Base =
`(7)/(2)` inches

Hence The length of side adjacent to the cosine angle is
`(7)/(2)` inches Answer

Answer 2

The length of the side adjacent to the angle is 3.5 inches

Explanation:

Here,given the cosine of an acute angle = 1/2

Let that acute angle be Ф

⇒ cos Ф = 1/2

Also,
`\cos  \theta = (Base)/(Hypotenuse)`

⇒
`(Base)/(Hypotenuse)  =  (1)/(2)`

or, the ratio of Base : Hypotenuse is 1 : 2

Now, Hypotenuse = 7 inches (given)

⇒
`(1)/(2)   =  (Base)/(7)   \implies Base = (7)/(2)  = 3.5`

Hence, the length of the side adjacent to the angle is 3.5 inches