Charlie is at a small airfield watching for the approach of a small plane with engine trouble. he sees the plane at an angle of elevation of 32. at the same time, the pilot radios charlie and reports the plane’s altitude is 1,700 feet. charlie’s eyes are 5.2 feet from the ground.

find the ground distance from charlie to the plane. show how you know.

Tan (32°) = 1700 feet / x => x = 1700 feet / tan(32°) = 1700 feet / 0.625 = 2720 feet.

2711.8 ft

Step-by-step explanation:

We know the horizontal and vertical distances here:

vertical distance = 1,700 feet.  In the right triangle formed by the horiz. and vert. distances and the hypotenuse, 1,700 ft is the side opposite the 32° angle of elevation of the plane.  We need to know the horiz. distance (ground distance).

The tangent function involves both the horiz. and the vert. distances:

tan Ф = opp / adj

and we can solve this for adj:  

          opp

adj =

         tan Ф

In this case we have:

          1700 ft          1700 ft

adj = =    = 2720.6 ft

           tan 32°         0.625

If we take into account the fact that Charlie's eyes are 5.2 ft from the ground, the problem solution becomes:

         (1700-5.2) ft         1694.8 ft

adj = =    = 2711.8 ft

           tan 32°                    0.625

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841