Question

Mark is running a marathon from point A to point B to point C and then back to point eight use the given diagram to find the dishes Mark run to successfully finish the race

Answer 1

Note: form the question, he ran from point A to B to C

Hence we will need to find DB, BC

From triangle CBD

`\begin{gathered} \text{Opp = }DB \\ \text{Adj = 60} \\ \theta\text{ = 27} \\ \text{ Using the Trig function} \\ \tan \theta\text{ = }\frac{\text{Opp}}{\text{Adj}} \\ \tan \text{ 27 = }(DB)/(60) \\ By\text{ cross multiply} \\ DB\text{ = tan 27 }*\text{ 60} \\ DB\text{ = 30.57meter} \\ \end{gathered}`

DB = 30.57

Step2: we will need to find CB still from triangle CBD

`\begin{gathered} CB\text{ = Hyp} \\ \text{Adj= 60 } \\ \theta\text{ = 27} \\ \cos \theta\text{ = }\frac{\text{Adj}}{\text{Hyp}} \\ \cos \text{ 27 = }(60)/(CB) \\ 0.8910\text{ =}(60)/(CB) \\ 0.8910* CB\text{= 60} \\ CB\text{ = }(60)/(0.8910) \\ CB\text{ =67.3meter} \end{gathered}`

CB = 67.3meter

STEP 3

From traingle ADC

From the triangle, we will need to find AB, AC

Step 4: we will need to find AC from still from triangle ABC

`\begin{gathered} \text{Hyp = AC} \\ Adj\text{ = 60} \\ \theta\text{ = 43} \\ \cos \text{ }\theta\text{ =}\frac{Adj}{\text{Hyp}} \\ \cos \text{ 43 = }(60)/(AC) \\ 0.731\text{ = }(60)/(AC) \\ 0.731\text{ }*\text{ AC = 60} \\ AC\text{ = }(60)/(0.731) \\ AC\text{ = 82.039} \\ \end{gathered}`

The Dishes distance. is the sum of all our answer

82.039 + 67.3 + 55.95 + 30.57 = 233.859meter