Let’s solve each problem one by one. We’ll use trigonometry — specifically, sine, cosine, and tangent — because these problems involve right triangles with angles of elevation or depression.
Remember:
-
Sine (sin) = opposite / hypotenuse
-
Cosine (cos) = adjacent / hypotenuse
-
Tangent (tan) = opposite / adjacent
We’ll round all answers to the nearest tenth as instructed.
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Problem 1:
A man flies a kite with a 100 foot string. The angle of elevation is 52°. How high off the ground is the kite?
This is a right triangle:
- Hypotenuse = 100 ft (string)
- Angle = 52°
- Opposite side = height we want → use
sine
sin(52°) = opposite / 100
→ opposite = 100 × sin(52°)
Calculate sin(52°): ≈ 0.7880
→ 100 × 0.7880 = 78.8
✔ Height =
78.8 feet
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Problem 2:
Brian’s kite is flying at the end of 65 m of string. Angle of elevation is 70°. How high above Brian’s head?
Again, right triangle:
- Hypotenuse = 65 m
- Angle = 70°
- Opposite = height → use
sine
sin(70°) = opposite / 65
→ opposite = 65 × sin(70°)
sin(70°) ≈ 0.9397
→ 65 × 0.9397 ≈ 61.0805 → round to
61.1
✔ Height =
61.1 meters
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Problem 3:
Airplane takes off in front of a 60 ft building. Angle of elevation from plane to top of building is 65°. How far away must the plane be to clear it safely?
Wait — this wording is tricky. “Angle of elevation from the plane to the top of the building” — that would mean the plane is looking *up* at the building? That doesn’t make sense if the plane is taking off. Probably meant: angle of elevation *from the ground* to the plane, but the diagram shows the plane on the ground and the building ahead.
Looking at the diagram description: plane on ground, building 60 ft tall, angle from plane to top of building is 65° — so yes, angle of elevation from plane (on ground) to top of building.
So:
- Opposite = 60 ft (building height)
- Angle = 65°
- Adjacent = distance from plane to base of building → use
tangent
tan(65°) = 60 / adjacent
→ adjacent = 60 / tan(65°)
tan(65°) ≈ 2.1445
→ 60 / 2.1445 ≈ 27.978 → round to
28.0
✔ Distance =
28.0 feet
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Problem 4:
Ladder scales a 13 ft wall. Angle of elevation from ground to top of wall is 36°. How long must the ladder be?
Right triangle:
- Opposite = 13 ft (wall height)
- Angle = 36°
- Hypotenuse = ladder length → use
sine
sin(36°) = 13 / hypotenuse
→ hypotenuse = 13 / sin(36°)
sin(36°) ≈ 0.5878
→ 13 / 0.5878 ≈ 22.116 → round to
22.1
✔ Ladder length =
22.1 feet
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Problem 5:
From a point 12 ft from base of flagpole, angle of elevation to top is 53°. How tall is the flagpole?
Right triangle:
- Adjacent = 12 ft
- Angle = 53°
- Opposite = height → use
tangent
tan(53°) = opposite / 12
→ opposite = 12 × tan(53°)
tan(53°) ≈ 1.3270
→ 12 × 1.3270 ≈ 15.924 → round to
15.9
✔ Flagpole height =
15.9 feet
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Problem 6:
A 5 ft ramp is needed. Angle of elevation must be 30°. How far from the base will you place the start of the ramp?
Ramp is the hypotenuse = 5 ft
Angle = 30°
We want the horizontal distance (adjacent) → use
cosine
cos(30°) = adjacent / 5
→ adjacent = 5 × cos(30°)
cos(30°) ≈ 0.8660
→ 5 × 0.8660 = 4.33 → round to
4.3
✔ Distance from base =
4.3 feet
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Final Answer:
1. 78.8 feet
2. 61.1 meters
3. 28.0 feet
4. 22.1 feet
5. 15.9 feet
6. 4.3 feet
Parent Tip: Review the logic above to help your child master the concept of worksheet angles of depression and elevation.
