Solving Real Life problems with right triangle application

1. 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

2. 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
Solution: 20o = 50m/stan
s = 50m/ tan20o
s = 137.37 m
The shadow
cast of a
building is
137.37m long

3. 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?
Real-Life Problem on right triangle

4. 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
Real-Life Problem on right triangle
Solution:
70o = h/12fttan
h= 12 tan70o
h = 32.97 ft.
The top of the ladder is
32.97 ft.

5. 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
Real-Life Problem on right triangle
Solution:
70o = 12ft/Lcos
L= 12 /cos70o
L = 35.09 ft.
The ladder is 35.09 ft.
long

6. Find the length of the chord
of a circle of radius 20cm
subtended by a central angle
of 150o?
Real-Life Problem on right triangle

7. Find the length of the chord of a circle of radius 20cm subtended by a
central angle of 150o?
Real-Life Problem on right triangle
The chord is 38.64cm long

8. A chord of a circle is 8.8 cm. Find the central angle of the chord if its
radius is 10.5 cm.
Real-Life Problem on right triangle
Then central angle is 50o
1
2
𝜃 = sin−1
(4.4 ÷ 10.5)
1
2
𝜃 = 24.77 𝑜

9. A man drives 500m along a
road which is inclined 20o to
the horizontal. How high
above his starting point is
he?
Real-Life Problem on right triangle
Answer: The car is 171m high from
the starting point.

10. A tree 100ft tall casts a
shadow 120ft long. Find the
angle of elevation of the sun.
Real-Life Problem on right triangle

11. Angle of elevation

12. Angle of Depression

13. A tree 100ft tall casts a shadow 120ft long. Find the angle of
elevation of the sun.
Real-Life Problem on right triangle
H
100ft
120ft
H = 100/120
Tan H = 100/120
H = tan-1 (100/120)
H = 40o

14. From the lighthouse 120m
above the sea, the angle of
depression of a boat is 15o.
How far is the boat from the
lighthouse?
Real-Life Problem on right triangle

15. From the lighthouse 120m above the sea, the angle of
depression of a boat is 15o. How far is the boat from the
lighthouse?
Real-Life Problem on right triangle
15o
120m
d -distance
15o=120/d
Tan 15o=120/d
d=120/Tan 15o
d =448 m

16. 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.
Real-Life Problem on right triangle

17. 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.
Real-Life Problem on right triangle
69.8o= h/118m
Tan 69.8o= h/118m
(118)(Tan 69.8o) = h
h=321 meters

18. If a kite is 150ft. high when 800ft. Of string is out,
what angle does the kite make with the ground?
Real-Life Problem on right triangle
800ft
150ft
A=150/800
Sin A=150/800
A= sin-1(150/800)
A= 110

19. 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.
Real-Life Problem on right triangle
v
x1=71.04m
x2=97.33m
d=26.29m
Answer: The distance of two boats
is 26.29m
32
24o15’ 18o12’
distance

20. 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?
Real-Life Problem on right triangle
250ft
21o
85ft 85ft
h2=h1+85
h1= 250tan21
h1= 96
h2=96+85 = 181ft

21. 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.
Real-Life Problem on right triangle
X1 = 2888
D = x2-2888