Question

Percal: Note Triangle may not be drawn to scale .

Answer 1

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=(opposite)/(adjacent) \end{gathered}`

By substitution,

`\begin{gathered} \tan78=(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=(adjacent)/(hypotenuse) \end{gathered}`

By substitution,

`\begin{gathered} \cos78=(6)/(c) \\ Cross\text{ multiply} \\ c\cdot\cos78=6 \\ c=(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}`