The angle of elevation to the top of a building is 21 degrees. At a point 80 feet closer, the angle of elevation to the top of the same building is 33 degrees. Approximate to the hudredth the height of the building.
Please explain how to sketch it and step by step how to solve it.
2007-05-13 11:48:36 · 2 answers · asked by yumi_yune 2 in Science & Mathematics ➔ Mathematics
basically you know that the height of the beuilding doesn't change, so it can be called "h". The distance from the building is unknown, so it can be called "x". Then set up two different right triangles, using x as your original distance, so you second distance would be "x-80". Then create an equation for each of the triangles, using cos (21) = x / h and cos (33) = (x-80) / h. This gives you two equations and two unknowns. Simply solve the system.
2007-05-13 11:56:36 · answer #1 · answered by badaerozepstones 3 · 0⤊ 0⤋
Angle of elevation is the angle from the horizontal ground to the top of the building. You have two readings, one from a point at an unknown distance from the building of 21 degrees. Then you move 80 feet closer and the angle is now 33 degrees.
We can apply the trig function Tangent to solve this.
For the 21 degree point Tan 21 = height/distance. We know neither.
For the 33 degree point Tan 33= height/(distance-80).
We read the tan readings from a table or your high-class TR?? calculator. We wind up with two equations with two unknowns, one of which is height.
2007-05-13 18:58:16 · answer #2 · answered by cattbarf 7 · 0⤊ 0⤋