Question

Percal: Note Triangle may not be drawn to scale .

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Redraw the given right triangle

STEP 2: Find the required measures

To get a

Using SOH CAH TOA

$\begin{gathered} \theta=78\degree,a=opposite=?,b=adjacent=6 \\ tan\theta=\frac{opposite}{adjacent} \end{gathered}$

By substitution,

$\begin{gathered} \tan78=\frac{a}{6} \\ Cross\text{ multiply} \\ a=6\cdot\tan78 \\ a=28.22778066 \\ a\approx28.23 \end{gathered}$

a = 28.23

To get c

$\begin{gathered} c=hypotenuse=?,b=adjacent=6,\theta=78\degree \\ \cos\theta=\frac{adjacent}{hypotenuse} \end{gathered}$

By substitution,

$\begin{gathered} \cos78=\frac{6}{c} \\ Cross\text{ multiply} \\ c\cdot\cos78=6 \\ c=\frac{6}{\cos78} \\ c=28.85840607 \\ \\ c\approx28.86 \end{gathered}$

c = 28.86

To get B

$\begin{gathered} A+B+C=180\degree----Angles\text{ in a triangle} \\ 78\degree+B+90=180\degree \\ B=180\degree-78\degree-90\degree \\ B=12\degree \end{gathered}$

Hence, the answers are given as:

$\begin{gathered} a=28.23 \\ c=28.86 \\ B=12\text{ }degree \end{gathered}$