Trigonometry Math Question Help??
A point on level ground is 20 m away from a point on the ground directly below a horizontal bridge that forms an overpass on a highway. The angle of elevation to the underside of the bridge is 14 degrees. Will the truck that is 4.3 m in height be able to pass safely under the bridge if the truck needs to have 0.5 m in clearance?
- TomVLv 711 months agoFavorite Answer
Bridge clearance = 20tan14° = 4.99 m
Required clearance = 4.3+0.5 = 4.8m
The truck can safely pass under the bridge.
- DavidLv 711 months ago
Yes because 20*tan(14) = 4.986 and 4.3+0.5 = 4.8
- electron1Lv 711 months ago
To safely pass under the bridge must be 4.8 meters below the bridge. This is the sum of the height of the bridge and the clearance. The height and the horizontal distance are the two sides of a right triangle. The ratio of these two numbers is equal to the tangent of the angle.
h ÷ 20 = tan 14
h = 20 * tan 14
This is approximately 5 meters. Since this is greater than the total clearance, the truck will pass safely under the bridge. I hope this is helpful for you.
- RealProLv 711 months ago
Yes 20tan14° > 4.8