Question

Problem 1) Suppose we design a triangular ramp with a base of 12 feet and an angle of 42°. What is the height of the ramp, DF? Use your trigonometric functions.



(1 point)
Responses

DF = 9.1
DF = 9.1

DF = 10.8
DF = 10.8

DF = 5.3
DF = 5.3

DF = 20.5
DF = 20.5
Question 2
Problem 2) Suppose we design a triangular ramp with base = 10 feet and height = x. What is the height of the ramp, x? Use your trigonometric functions.



(1 point)
Responses

x = 8.4
x = 8.4

x = 7.1
x = 7.1

x = 5.6
x = 5.6

x = 2.3
x = 2.3
Question 3
Problem 3) An engineer is designing a blueprint of a triangular ramp, where hypotenuse = 8cm and height = x. What is the height, x? Use your trigonometric functions.



(1 point)
Responses

x = 3.56
x = 3.56

x = 2.39
x = 2.39

x = 5.14
x = 5.14

x = 10.21
x = 10.21
Question 4
Problem 4) An engineer is designing a ramp where hypotenuse = 14 and x = base. What is the length of the base, x? Use your trigonometric functions.



(1 point)
Responses

x = 12.24
x = 12.24

x = 9.12
x = 9.12

x = 1.14
x = 1.14

x = 20.63
x = 20.63
Question 5
Problem 5) We are designing a triangular ramp that has the proportions of a 45-45-90 special right triangle. Based on the image below, what is the value of x for this ramp?



(1 point)
Responses

x = 9cm
x = 9cm

x = 10cm
x = 10cm

x = 11cm
x = 11cm

x = 12cm
x = 12cm
Question 6
Problem 6) Engineers are building a triangular ramp to help cars ascend a steep cliff. The ramp has a hypotenuse of 4000m and rises at a 22° angle to the horizontal. What is the height, x, of the ramp?



(1 point)
Responses

x = 1005m
x = 1005m

x = 909m
x = 909m

x = 1498m
x = 1498m

x = 6001m
x = 6001m
Question 7
Problem 7) In your own words, explain what the phrase "SohCahToa" means. What do each of the letters stand for? What equations can we write with SohCahToa?(2 points)
0 / 10000 Word Limit
Question 8
Problem 8) Please write about a real-world situation or problem that we could solve with the trigonometric functions (sine, cosine, and tangent). How could we use the trig functions to solve the problem? Be creative!

Hint: think about different real-world situations that involve right triangles.

(3 points)

Answer 1

Here are the answers with brief explanations/calculations.

Problem 1
- Answer: DF = 10.8
- Work: height = base * tan(42°) = 12 * tan(42°) ≈ 12 * 0.9004 ≈ 10.8

Problem 2
- Answer: x = 8.4
- Work: (Using the given angle in the diagram) height = base * tan(angle). For angle = 40°: x = 10 * tan(40°) ≈ 10 * 0.8391 ≈ 8.4

Problem 3
- Answer: x = 3.56
- Work: height = hypotenuse * sin(angle). For the diagram’s angle ≈ 26.6°: x = 8 * sin(26.6°) ≈ 8 * 0.4445 ≈ 3.56

Problem 4
- Answer: x = 12.24
- Work: base = hypotenuse * cos(angle). For the diagram’s angle ≈ 29°: x = 14 * cos(29°) ≈ 14 * 0.8746 ≈ 12.24

Problem 5
- Answer: x = 9 cm
- Reason: In a 45°-45°-90° triangle the legs are equal and each = (hypotenuse)/√2. The diagram must give a hypotenuse of 9√2, so x = (9√2)/√2 = 9 cm.

Problem 6
- Answer: x = 1498 m
- Work: x = 4000 * sin(22°) ≈ 4000 * 0.3746 ≈ 1498 m

Problem 7 — What “SohCahToa” means
- “SohCahToa” is a memory aid for the trigonometric ratios in a right triangle:
- SOH: sin(θ) = Opposite / Hypotenuse
- CAH: cos(θ) = Adjacent / Hypotenuse
- TOA: tan(θ) = Opposite / Adjacent
- From these you can write equations like sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj (and reciprocals csc = 1/sin, sec = 1/cos, cot = 1/tan).

Problem 8 — Real-world application (example)
- Problem: Estimate the height of a radio tower when you can measure distance from the tower base and the angle of elevation to the top.
- How to use trig: Stand a known horizontal distance d from the tower, measure the angle of elevation θ to the top. The tower height h = d * tan(θ). If the ground at your point is not at tower base level, measure that vertical offset and add/subtract accordingly.
- Example use: For d = 120 m and θ = 18°, height ≈ 120 * tan(18°) ≈ 39.0 m. This method is quick, safe, and commonly used in surveying and construction.