Chapter 9.9, Problem 5PSA

To determine

To calculate: The cosine of an angleM .

Answer to Problem 5PSA

The cosine of an angleM is $\frac{4}{5}$ .

Explanation of Solution

Given information:

  $\tan \angle E=\frac{3}{4}$

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

  $\tan \theta =\frac{oppositeside}{adjacentside}$

  $cos\theta =\frac{adjacentside}{hypotenuseside}$

Calculation:

  $\tan \angle E=\frac{3}{4}$

We know that $\tan \theta =\frac{oppositeside}{adjacentside}$

Thus opposite side = 3 and adjacent side = 4.

  

Side MO can be calculated by applying Pythagoras Theorem.

In right angle triangle MNO , we get

  $\begin{array}{l}$ {(MO)}^2={(MN)}^2+{\left(NO\right)}^2$$ {(MO)}^2={(4)}^2+{\left(3\right)}^2$$ {(MO)}^2=16+9$\therefore MO=\sqrt{25}\\ \therefore MO=5\end{array}$

  $cos\angle M=\frac{adjacentside}{hypotenuseside}=\frac{MN}{OM}=\frac{4}{5}$