From two tracking stations, A and B, 450km apart, a satellite is sighted at C directly above the line joining A to B. At the moment of sighting, angle A is 39 and angle B is 45. Find the height of the satellite.
Please show all your steps clearly and asap,
Thanks
3(4a+1)-6_>10a-7
To find the height of the satellite, we can use trigonometry and create a right-angled triangle using the given information.
Let's start by labeling the points:
- Let A be the tracking station on the left side.
- Let B be the tracking station on the right side.
- Let C be the position directly above the line joining A to B.
We can form a right-angled triangle with the following sides:
- The side opposite angle A is the height of the satellite.
- The side opposite angle B is the height of the satellite plus the Earth's radius.
- The hypotenuse is the distance between the two tracking stations, which is 450 km.
Step 1: Calculate the length of side AB using the law of cosines.
c^2 = a^2 + b^2 - 2ab * cos(C)
AB^2 = (satellite height + Earth's radius)^2 + (satellite height + Earth's radius)^2 - 2(satellite height + Earth's radius)(satellite height + Earth's radius) * cos(45)
= (satellite height + Earth's radius)^2 + (satellite height + Earth's radius)^2 - 2(satellite height + Earth's radius)(satellite height + Earth's radius) * 0.7071
Step 2: Calculate the length of side AC using the sine function.
sin(A) = opposite/hypotenuse
sin(39) = satellite height / AB
satellite height = AB * sin(39)
Step 3: Substitute the value of AB from Step 1 into the equation of Step 2 to find the satellite height.
Note: We need to know the value of the Earth's radius in order to calculate the satellite height accurately.