Answer:
3315.03 meters.
Step-by-step explanation:
We have been given a blimp is 1100 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. We are asked to find the distance between both stadiums.
First of all, we will find the distance between 1st stadium and base of blimp. We can see that stadium and blimp forms a right triangle with respect to ground, where m is adjacent side and 1100 meters is opposite side for 75.2 degrees angle. So we can set an equation as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(75.2^{\circ})=\frac{1100}{m}[/tex]
[tex]m=\frac{1100}{\text{tan}(75.2^{\circ})}[/tex]
[tex]m=\frac{1100}{3.784848088366}[/tex]
[tex]m=290.632536[/tex]
Similarly, we will find value of x as:
[tex]\text{tan}(17.9^{\circ})=\frac{1100}{m+x}[/tex]
[tex]\text{tan}(17.9^{\circ})=\frac{1100}{290.632536+x}[/tex]
[tex]290.632536+x=\frac{1100}{\text{tan}(17.9^{\circ})}[/tex]
[tex]290.632536+x=\frac{1100}{0.322991199346}[/tex]
[tex]290.632536+x=3405.6655482[/tex]
[tex]290.632536-290.632536+x=3405.6655482-290.632536[/tex]
[tex]x=3115.033[/tex]
[tex]x\approx 3115.03[/tex]
Therefore, the two stadiums are approximately 3115.03 meters apart.
