Hot Road
A hot-air balloon is floating above a straight road.?
A hot-air balloon is floating above a straight road.?
To calculate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon.The angles of depression are found to be 17 degrees & 20 degrees. How high in feet is the ballon? [1 mile=5280]
Draw a picture. You have the balloon and two mile-posts, they form a triangle. The height of the balloon is a line, perpendicular to the road, that bisects this triangle into two smaller triangles.
Using the the two angles of depression and the rule about similar triangles, you can work out the angles between the vertical height and the larger triangle at the balloon.
Now you need the rule of Sines: a/SIN A = b/SIN B = c/SIN C
You have all three angles of the large triangle and one side (5280ft) so using the rule of Sines you can work out the length of the other two sides of the larger triangle (mile-post to balloon to mile-post).
Now you are left with two right-angled triangles of which you know all three angles and one side (which you just calculated). So now you can use the rule of Sines again to work out the length of the perpendicular side - and that's the height of the balloon
Hot rod (1979) car chase with crash
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