1. Day 4: Right Angle Triangle Word Problems
Unit 8: Trigonometry

2. Learning Goals
To be able to solve word problems involving right triangles

3. A radio dish sits on top of a 100 m tower, with the vertex of the dish 9 m above the top of the tower. The radar shows an approaching plane to be 50 km away, along a 20° angle of elevation. Find the plane’s altitude and ground distance from the tower.

4. Angle of Elevation
The angle created from the horizontal looking up

5. Angle of Depression
The angle created from the horizontal looking down

6. 50 km 20° 9 m Ground distance Altitude 100 m
A radio dish sits on top of a 100 m tower, with the vertex of the dish 9 m above the top of the tower. The radar shows an approaching plane to be 50 km away, along a 20° angle of elevation. Find the plane’s altitude and ground distance from the tower.
50 km
20°
9 m
Ground distance
Altitude
100 m

7. Ground distance is 46,984.6 m or 46.98 km.
A radio dish sits on top of a 100 m tower, with the vertex of the dish 9 m above the top of the tower. The radar shows an approaching plane to be 50 km away, along a 20° angle of elevation. Find the plane’s altitude and ground distance from the tower.
cos 20 = 𝑥 50000
𝑥=50000 cos 20
𝑥= m
Ground distance is 46,984.6 m or km.
100 m
9 m
50 km
Altitude
Ground distance
20°

8. sin 20 = 𝑦 50000 𝑦=50000 sin 20 𝑦=17101 m Altitude =100+9+17101
A radio dish sits on top of a 100 m tower, with the vertex of the dish 9 m above the top of the tower. The radar shows an approaching plane to be 50 km away, along a 20° angle of elevation. Find the plane’s altitude and ground distance from the tower.
sin 20 = 𝑦 50000
𝑦=50000 sin 20
𝑦=17101 m
Altitude =
Altitude =17,210 m
Altitude is 17,210 m or km.
100 m
9 m
50 km
Altitude
Ground distance
20°

9. A searchlight is mounted at the front of a helicopter
A searchlight is mounted at the front of a helicopter. It is 150 m above the ground and the top of the beam is angled at 70° from horizontal. The beam spreads out at an angle of 5°. How wide is the ground that the beam illuminates?

10. A searchlight is mounted at the front of a helicopter
A searchlight is mounted at the front of a helicopter. It is 150 m above the ground and the top of the beam is angled at 70° from horizontal. The beam spreads out at an angle of 5°. How wide is the ground that the beam illuminates?
70°
15° 5°
150 m x y

11. A searchlight is mounted at the front of a helicopter
A searchlight is mounted at the front of a helicopter. It is 150 m above the ground and the top of the beam is angled at 70° from horizontal. The beam spreads out at an angle of 5°. How wide is the ground that the beam illuminates?
tan 15 = 𝑥 150
𝑥=150 tan 15
𝑥=40.2 m
150 m
70° 5°
15° x y

12. A searchlight is mounted at the front of a helicopter
A searchlight is mounted at the front of a helicopter. It is 150 m above the ground and the top of the beam is angled at 70° from horizontal. The beam spreads out at an angle of 5°. How wide is the ground that the beam illuminates?
tan 20 = 𝑧 150
𝑧=150 tan 20
𝑧=54.6 m
150 m
70° 5°
15° x y

13. Therefore the beam of light covers a width of 14.4 m.
A searchlight is mounted at the front of a helicopter. It is 150 m above the ground and the top of the beam is angled at 70° from horizontal. The beam spreads out at an angle of 5°. How wide is the ground that the beam illuminates?
𝑦=𝑧−𝑥
𝑦=54.6−40.2
𝑦=14.4 m
Therefore the beam of light covers a width of 14.4 m.
150 m
70° 5°
15° x y

14. Holly bought a new house with a triangular shaped lawn
Holly bought a new house with a triangular shaped lawn. She wants to cover the lawn with sod. How much will it cost to sod the lawn at $1.50/ m 2 ?
120 m h
40°
100 m

15. Holly bought a new house with a triangular shaped lawn
Holly bought a new house with a triangular shaped lawn. She wants to cover the lawn with sod. How much will it cost to sod the lawn at $1.50/ m 2 ?
sin 40 = ℎ 120
ℎ=120 sin 40
ℎ=77.1 m
120 m
100 m
40° h

16. It would cost $5,782.50 to sod her lawn.
Holly bought a new house with a triangular shaped lawn. She wants to cover the lawn with sod. How much will it cost to sod the lawn at $1.50/ m 2 ?
𝐴= 1 2 𝑏ℎ
𝐴= 1 2 (100)(77.1)
𝐴=3855 m2
Cost =3855×1.50 =
It would cost $5, to sod her lawn.
120 m
100 m
40° h

17. Success Criteria
I CAN solve word problems involving right triangles using:
Sum of angles
Pythagorean Theorem
SOHCAHTOA

18. To Do…
Worksheet
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