I need help with # 13,14,15 and 16 please!

Mathematics
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Oct 4th, 2014

13.     Angle = 72 degrees

        Dixtance = x = 30 m

       Height = h = ?

Now      tan x = h / x

Putting the values, we get

tan (72 degree) = h / 30

h = 30 * tan (72 degree)

h = 30 * 3.077

h = 92.33 m

14.        The angle of depression decreases.

15.       Height = h = 1500 ft

            Angle = 25 degrees

          Distance = ?

 As      tan x = Distance / 1500

Now 

tan (25 degree) = Distance / 1500

Distance = 1500 * tan (25 degree)

Distance = 1500 * 0.466

Distance = 699.46 m

Now Sine x = Distance / Shortest Distance

Sine x = Distance / Shortest Distance

Shortest Distance = Distance / Sine x

Putting the values, we get

Shortest Distance = 699.46 / Sine (25 degree)

Shortest Distance = 699.46 / 0.4226

Shortest Distance = 1655.1 m

16.   Distance = 20 ft 

        Angle = 35 degree

      Height of shorter building = 120 ft 

      Height of taller building = ?

      Height of taller building = 120 + x

Now   tan x = (120 + x) / Distance

Putting the values, we get

tan (35 degree) = (120 + x) / 20

0.7002 = (120 + x) / 20

Now

0.7002 * 20 = 120 + x

14.004 = 120 + x

x = 120 - 14.004

x = 105.996

Now 

Height of Taller building = 120 + (105.996)

Height of Taller building = 225.996 m 

Oct 4th, 2014

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Oct 4th, 2014
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Oct 4th, 2014
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