Question

1. Given d = 25,01 = 15°, and O2 = 40°. Find x and h. Show work. Round to 2 decimal places.0,

Answer 1

Let's check first this right triangle from the figure:

We have, using tangent on the angle:

`\begin{gathered} \tan (15^o)=(h)/(25+x) \\ \Rightarrow h=0.268(25+x) \end{gathered}`

And then, looking at the other right triangle:

Doing the same as before, we have that:

`\begin{gathered} \tan (40)\text{ = }(h)/(x) \\ \Rightarrow h=0.839x \end{gathered}`

Now, we can use both equations of h to solve for x:

`\begin{gathered} 0.268(25+x)=0.839x \\ \Rightarrow6.7+0.268x=0.839x \\ \Rightarrow6.7=0.571x\Rightarrow x=(6.7)/(0.571)=11.73 \end{gathered}`

Which we can finally use to find h in any equation:

`\begin{gathered} h=0.268(25+11.73)=9.843 \\ or \\ h=0.839\cdot11.73=9.841 \end{gathered}`