Math 2 Quiz: Diagramming For Modeling
4 questions · exam conditions
0:00
Diagramming For ModelingQuestion 1 of 4

A water tower's height is being measured using two observation points. From point A, 200 meters from the tower's base, the angle of elevation is 25°. From point B, 350 meters from the tower's base (on the opposite side), the angle of elevation is 18°. Which diagram labeling correctly identifies the relationship needed to verify the tower height using both measurements?

Two separate right triangles: Triangle 1 has adjacent = 200m, angle = 25°; Triangle 2 has adjacent = 350m, angle = 18°; both should give same tower height using tangent
Single triangle with tower height as opposite side, base = 550m, and angles 25° and 18° at the endpoints, using sine rule to find height
Two right triangles sharing hypotenuse: Triangle 1 has opposite = 200m, angle = 25°; Triangle 2 has opposite = 350m, angle = 18°; solve using tangent
Isosceles triangle with tower as altitude, base segments 200m and 350m, vertex angles 25° and 18°, using cosine rule for height verification
← Back to quizzes

Math 2 Quiz

Math 2 Quiz: Diagramming For Modeling

Practice Diagramming For Modeling in Math 2 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Diagramming For Modeling, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 2.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A water tower's height is being measured using two observation points. From point A, 200 meters from the tower's base, the angle of elevation is 25°. From point B, 350 meters from the tower's base (on the opposite side), the angle of elevation is 18°. Which diagram labeling correctly identifies the relationship needed to verify the tower height using both measurements?

  1. Two separate right triangles: Triangle 1 has adjacent = 200m, angle = 25°; Triangle 2 has adjacent = 350m, angle = 18°; both should give same tower height using tangent (correct answer)
  2. Single triangle with tower height as opposite side, base = 550m, and angles 25° and 18° at the endpoints, using sine rule to find height
  3. Two right triangles sharing hypotenuse: Triangle 1 has opposite = 200m, angle = 25°; Triangle 2 has opposite = 350m, angle = 18°; solve using tangent
  4. Isosceles triangle with tower as altitude, base segments 200m and 350m, vertex angles 25° and 18°, using cosine rule for height verification
Explanation: Each observation point creates a separate right triangle with the tower. Point A: tan(25°) = h/200, Point B: tan(18°) = h/350. Both calculations should yield the same tower height h, providing verification of the measurement.

Question 2

Two buildings of different heights cast shadows when the sun is at a 42° angle of elevation. Building A is 85 feet tall and casts a 90-foot shadow. Building B casts a 75-foot shadow. Which proportional setup correctly uses the known quantities to find Building B's height?

  1. 8590=h75\frac{85}{90} = \frac{h}{75} where the ratio of height to shadow length is constant for both buildings (correct answer)
  2. 9085=75h\frac{90}{85} = \frac{75}{h} where the ratio of shadow to height length is constant for both buildings
  3. 8575=90h\frac{85}{75} = \frac{90}{h} where the ratio of Building A height to Building B shadow equals Building A shadow to Building B height
  4. 4285=42h\frac{42}{85} = \frac{42}{h} where the sun angle creates proportional relationships between heights
Explanation: Since both buildings are measured under the same sun angle, the ratio of height to shadow length must be the same for both buildings. Building A: 85/90, Building B: h/75. Setting them equal: 85/90 = h/75.

Question 3

A surveyor uses a clinometer to measure the angle of depression to a river from a cliff. Standing 180 feet above the river, she measures a 15° angle of depression to a point on the opposite bank. The horizontal distance from the base of her cliff to the river edge is 45 feet. Which labeling correctly identifies the setup for finding the width of the river?

  1. Known: height = 180 ft, angle of depression = 15°, cliff distance = 45 ft; Unknown: river width = x, using tan(15°) = 180/(45 + x)
  2. Known: height = 180 ft, angle of elevation = 15°, cliff distance = 45 ft; Unknown: river width = x, using tan(15°) = (45 + x)/180
  3. Known: height = 180 ft, angle of depression = 15°, cliff distance = 45 ft; Unknown: total distance = x, using tan(15°) = 180/x, then river width = x - 45 (correct answer)
  4. Known: height = 180 ft, angle of depression = 15°, cliff distance = 45 ft; Unknown: river width = x, using sin(15°) = 180/(45 + x)
Explanation: The angle of depression from the cliff to the opposite bank creates a right triangle. The height is 180 ft (opposite) and the total horizontal distance is x (adjacent). Using tan(15°) = 180/x gives the total distance, then subtract 45 ft to get river width.

Question 4

Two similar triangles are used to model the shadow cast by a flagpole. A 6-foot person casts a 4-foot shadow at the same time a flagpole casts a 28-foot shadow. Which proportion setup correctly identifies the known and unknown quantities for finding the flagpole height?

  1. person heightperson shadow=flagpole shadowflagpole height\frac{\text{person height}}{\text{person shadow}} = \frac{\text{flagpole shadow}}{\text{flagpole height}} where 64=28h\frac{6}{4} = \frac{28}{h}
  2. person heightperson shadow=flagpole heightflagpole shadow\frac{\text{person height}}{\text{person shadow}} = \frac{\text{flagpole height}}{\text{flagpole shadow}} where 64=h28\frac{6}{4} = \frac{h}{28} (correct answer)
  3. person shadowperson height=flagpole heightflagpole shadow\frac{\text{person shadow}}{\text{person height}} = \frac{\text{flagpole height}}{\text{flagpole shadow}} where 46=h28\frac{4}{6} = \frac{h}{28}
  4. person heightflagpole height=person shadowflagpole shadow\frac{\text{person height}}{\text{flagpole height}} = \frac{\text{person shadow}}{\text{flagpole shadow}} where 6h=428\frac{6}{h} = \frac{4}{28}
Explanation: For similar triangles, corresponding sides are proportional. The ratio of height to shadow length must be the same for both objects. So person height/person shadow = flagpole height/flagpole shadow, giving 6/4 = h/28.