Question

Satellites KA-1212 and SAL-11 have spotted a UFO. Scientists want to determine its distance from KA-1212 so they can later determine its size. The distance between the satellites is 900 km. If KA-1212's camera is focused on SAL-11 , it must rotate 60° to see the UFO. If SAL-11's camera is focused on KA-1212, it must rotate 75°​​ to see the UFO. How far is the UFO from KA-1212?  Round your answer to the nearest kilometer.

Answer 1

Answer:

The distance of UFO from KA-1212 is 1229.7 km.

Step-by-step explanation:

We are given that,

Distance between the satellites = 900 km

Angle made by the satellite KA-1212 = 60°

Angle made by the satellite SAL-11 = 75°

So, from the figure below,

The third angle is given by = 180° - (60°+75°) = 180° - 135° = 45°

Then, using the law of sines, we have,

$\dfrac{x}{\sin 75}=\dfrac{900}{\sin 45}\\\\x=\dfrac{900\times \sin 75}{\sin 45}\\\\x=\dfrac{900\times 0.966}{0.707}\\\\x=\dfrac{869.4}{0.707}\\\\x=1229.7$

Thus, the distance of UFO from KA-1212 is 1229.7 km.

Answer 2

Use the sine rule. The two satellites form the base of a triangle with the UFO at the vertex. The sides of the triangle are KA-1212 joined to the UFO, and we call this side k, and the third side is SAL-11 joined to the UFO. The vertex angle is 180-(60+75)=45.
k/sin75=900/sin45 so k=900sin75/sin45=1229km approx.