# Trigonometry

posted by .

2 questions:

An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. Given the formula H=dtan times theta, where H is the height of the plane and d is the distance (along the ground) the plane has flown, find the angle of ascent theta at which the plane took off.

• Trigonometry -

H = d tan0
tan0 = H/d = 500 ft/10,560 ft = .04735
0 = 2.71 degrees

• Trigonometry -

"0" was supposed to be the symbol theta in my previous post

• Trigonometry -

I want to expand drwls' reply.

First, convert 2 miles to feet.

If 1 mile = 5280, then 2 miles = 10,560 feet.

Secondly, you must re-arrange the given formula because we are looking for an angle NOT height or distance on ground.

Let t = theta FOR SHORT.

tan(t) = 500ft/2 miles

tan(t) = 500ft/10,560ft

tan(t) = 0.047348485

Since we are looking an an angle, you must use the tangent invere key on your calculator. By the way, you must ALWAYS use the inverse key when searching for a trig function. I will do this in just a minute.

Before dealing with the angle itself, the decimal number 0.047348485 must be rounded to the nearest hundred- thousandths; it becomes 0.04735.

We now have:

tan(t) = 0.04735 We take the tangent inverse of the right side of the equation.

NOTE: tan^-1 is read: "tangent inverse" NOT tangent to the negative one. Is this clear?

t = tan^-1(0.04735)

t = 2.71 degrees

NOTE: I rounded 2.710843763 to the nearest hundreths and the answer became 2.71 degrees. This is what drwls did without going into detail.

I think detail is vital when tutoring online.

Done!

## Similar Questions

1. ### math

after take off an airplane is flying at a height of 8,000 feet above ground.It has traveled a distance of 10,000 feet from the airport.if sam was to spot under the airplane ,how far would he have to travel?
2. ### Calculus

Assume that an airplane is flying toward you at a constant height, h miles and at a speed dx/dt. When the plane is x miles away, what is the rate of change of theta?
3. ### precalculus

A model airplane 50 feet above the ground is flying away from an observer. Find the angle of elevation theta of the plane as a function of the distance from the observer to the plane. What is theta when the plane is 300 feet from the …
4. ### math

A ball is thrown into the air with an upward velocity of 20 ft/s. Its height (h) in feet after t seconds is given by the function h(t) = –16t^2 + 20t + 2. How long does it take the ball to reach its maximum height?
5. ### Word problem

. A catapult launches a boulder with an upwark velocity pf 184 feet per second. the heigh of the boulder in feet after t seconds is given by the function h(t)=-16t^2+184t+20. how long does it take the boulder to reach its maximum height?
6. ### Math help

A catapult launches a boulder with an upwark velocity pf 184 feet per second. the heigh of the boulder in feet after t seconds is given by the function h(t)=-16t^2+184t+20. how long does it take the boulder to reach its maximum height?
7. ### Algebra 1

Key: *** = my answer 8. A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = –16t2 + 148t + 30. How long does it take the boulder to …
8. ### Math

A model airplane is shot up from a platform 1 foot above the ground with an initial upward velocity of 56 feet per second. The height of the airplane above ground after t seconds is given by the equation h=-16t^+56t+1, where h is the …
9. ### Math

Please help ! 1.)a catapult launches a boulder with an upward velocity of 122 feet per second. the height of the boulder, h, in feet after t seconds is givin by the function h(t)=-16t^2+122t+10. what is the boulders maximum height …
10. ### Algebra

1.A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h=-16t^2+120t+10. How long does it take to reach maximum height?

More Similar Questions