right triangles Application

When the sun is 20o above the horizon, how long is the shadow cast by a building 50m high?

Real-Life Problem on right triangle

When the sun is 20o above the horizon, how long is the shadow cast by a building 50m high?


Solution:

20o = 50m/s

tan

s = 50m/ tan20o s = 137.37 m

The shadow cast of a building is 137.37m long

A ladder leans against the side of the building with its foot 12ft from the building. How far from the ground is the top of the ladder and how long is the ladder if it makes an angle of 70o with the ground?




Solution: 70o =

h/12ft tan h= 12 tan70o

h = 32.97 ft.

The top of the ladder is 32.97 ft.



Solution: 70o =

12ft/Lcos L= 12 /cos70o

L = 35.09 ft.

The ladder is 35.09 ft. long

Find the length of the chord of a circle of radius 20cm subtended by a central angle of 150o?


Find the length of the chord of a circle of radius 20cm subtended by a central angle of 150o?


The chord is 38.64cm long

A chord of a circle is 8.8 cm. Find the central angle of the chord if its radius is 10.5 cm.


Then central angle is 50o

12𝜃=24.77𝑜

A man drives 500m along a road which is inclined 20o to the horizontal. How high above his starting point is he?


Answer: The car is 171m high from the starting point.

A tree 100ft tall casts a shadow 120ft long. Find the angle of elevation of the sun.


Angle of elevation

Angle of Depression

A tree 100ft tall casts a shadow 120ft long. Find the angle of elevation of the sun.


H

100ft

120ft

H = 100/120

Tan H = 100/120

H = tan-1 (100/120)

H = 40o

From the lighthouse 120m above the sea, the angle of depression of a boat is 15o. How far is the boat from the lighthouse?


From the lighthouse 120m above the sea, the angle of depression of a boat is 15o. How far is the boat from the lighthouse?


15o

120m

d -distance

15o=120/d Tan 15o=120/d d=120/Tan 15o

d =448 m

The angle of elevation from a point 118 meters from the base of a tower to the top of the tower is 69.8o. Find the approximate height of the tower.


The angle of elevation from a point 118 meters from the base of a tower to the top of the tower is 69.8o. Find the approximate height of the tower.


69.8o= h/118m

Tan 69.8o= h/118m

(118)(Tan 69.8o) = h

h=321 meters

If a kite is 150ft. high when 800ft. Of string is out, what angle does the kite make with the ground?


800ft150ft

A=150/800Sin A=150/800 A= sin-1(150/800) A= 110

The angle of depression of boat A from the top of a cliff which is 32 m high is 24o15’. The angle of depression of boat B from the same point is 18o12’. Find the distance between the two boats.


v

x1=71.04m

x2=97.33m

d=26.29m

Answer: The distance of two boats is 26.29m

32

24o15’ 18o12’

distance

Two buildings are 250ft apart. The angle of elevation from the top of the shorter building to the top of the other building is 21o. If the shorter building is 85ft high, how high is the taller building?


250ft

21o

85ft 85ft

h2=h1+85

h1= 250tan21

h1= 96

h2=96+85 = 181ft

The angle of depression of one side of the lake, measured from a balloon 2600 feet above the lake is 42o. The angle of depression to the opposite side of the lake is 28o. Find the width of the lake.


X1 = 2888

D = x2-2888

right triangles Application

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