Question

What is the length x of the side of the triangle below? (Hint: Use the cosine function.)

A. 1.9
B. 2.4
C. 1.6
D. 2.1

Answer 1

The correct answer is A.

Step-by-step explanation

The given triangle is a right triangle.

The length of the hypotenuse is
`2.5` units.

The given angle is
`39\degree`.

The unknown side
`x` is adjacent to the given angle.

We can therefore use the cosine function to find
`x`.

Recall the mnemonics CAH.

This means that;

`\cos\theta=(Adjacent)/(Hypotenuse)`

This implies that,

`\cos39\degree=(x)/(2.5)`

We multiply both sides by
`2.5` to get,

`2.5\cos39\degree=x`

`x=2.5(0.7771)`

We evaluate to get

`x=1.94`

Therefore the length
`x` of the side of the triangle is
`1.9` units to the nearest tenth.