A tree casts a shadow 18 feet long. At the same time, a 5-foot-tall fence post casts a shadow 3 feet long. How tall is the tree?
A36 feet
B30 feet
C27 feet
D24 feet
Explanation
The tree and fence post form similar triangles with their shadows (same sun angle). tree height / tree shadow = fence height / fence shadow h / 18 = 5 / 3 h = 18 × 5/3 = 30 feet.
Question 3 of 10
Florida standards 6A-6EEasy Calc Word Diagram
In the triangle below, ∠A = 55° and ∠B = 65°. What is the measure of ∠C?
A70°
B60°
C75°
D50°
Explanation
📌 Step 1: Recall the Triangle Angle Sum Theorem All angles in a triangle add up to 180°.
📌 Step 2: Set up the equation ∠A + ∠B + ∠C = 180° 55° + 65° + ∠C = 180°
📌 Step 3: Solve ∠C = 180° − 55° − 65° = 60°
💡 Quick check: 55 + 65 + 60 = 180° ✓
Question 4 of 10
Florida standards 3A-3DHard Calc Word
Point Q(4, −1) is first reflected across the y-axis, then rotated 180° about the origin. What is the final image?
A(4, −1)
B(4, 1)
C(−4, −1)
D(−4, 1)
Explanation
📌 Step 1: Understand rigid motions (isometries) Transformations that preserve BOTH size and shape: ✅ Translation (slide) ✅ Reflection (flip) ✅ Rotation (turn)
📌 Answer:Translation preserves both size and shape.
💡 Key term: Rigid motions are also called "isometries" (iso = same, metry = measure).
Question 5 of 10
Florida standards 2A-2CMedium Calc Word Diagram
Find the distance between points P and Q shown on the coordinate plane below.
A5
B√13
C√17
D√10
Explanation
📌 Step 1: Apply the distance formula d = √((x₂ − x₁)² + (y₂ − y₁)²)
📌 Step 2: Plug in P(1, 2) and Q(−1, −1) d = √((1 − (−1))² + (2 − (−1))²) = √(2² + 3²) = √(4 + 9)
📌 Answer: d = √13 ≈ 3.61
💡 Tip: Leave your answer in √ form when exact values are expected on the CBE.
Question 6 of 10
Florida standards 12A-12EMedium Calc Word Diagram
A tangent line touches circle O at point T. OT = 5 and the external point P is 13 units from the center O. What is the length of tangent segment PT?
A12
B8
C14
D10
Explanation
The tangent is perpendicular to the radius at the point of tangency. Using the Pythagorean theorem: PT = √(OP² − OT²) = √(13² − 5²) = √(169 − 25) = √144 = 12.
Question 7 of 10
Florida standards 1A-1GHard Calc Word
A flagpole casts a shadow 15 feet long. At the same time, a 6-foot person standing nearby casts a shadow 4 feet long. How tall is the flagpole?
A24.0 feet
B20.0 feet
C18.0 feet
D22.5 feet
Explanation
📌 Step 1: Recognize similar triangles The sun creates the same angle for both the flagpole and the person, making two similar triangles.
📌 Step 2: Set up the proportion flagpole height / flagpole shadow = person height / person shadow h / 15 = 6 / 4
📌 Step 3: Cross-multiply and solve h × 4 = 15 × 6 4h = 90 h = 22.5 feet
💡 Tip: Shadow problems always use similar triangles because the sun's rays are parallel.
Question 8 of 10
Florida standards 1A-1GEasy Calc Word
A cylindrical water tank has a radius of 3 feet and a height of 8 feet. What is the volume of the tank? (Use π ≈ 3.14)
A226.08 ft³
B301.44 ft³
C150.72 ft³
D75.36 ft³
Explanation
📌 Step 1: Recall the volume formula for a cylinder V = πr²h
📌 Step 2: Plug in the values r = 3 ft, h = 8 ft, π ≈ 3.14 V = 3.14 × 3² × 8 = 3.14 × 9 × 8
💡 Tip: Always check your units — volume is measured in cubic units (ft³, cm³, m³).
Question 9 of 10
Florida standards 5A-5DEasy Calc Word Diagram
The exterior angle of a triangle is 140°. One of the non-adjacent interior angles is 65°. What is the other non-adjacent interior angle?
A40°
B115°
C65°
D75°
Explanation
📌 Step 1: Recall the Exterior Angle Theorem The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
📌 Step 2: Set up the equation exterior angle = angle A + angle C 140° = 65° + angle C
📌 Step 3: Solve angle C = 140° − 65° = 75°
💡 Tip: The Exterior Angle Theorem is a shortcut! You don't need to find the interior angle at B first. The exterior angle always equals the sum of the two "remote" interior angles.
Question 10 of 10
Florida standards 1A-1GMedium Calc Word Diagram
Quadrilateral ABCD has the properties shown below. Which type of quadrilateral is ABCD?
ARectangle
BParallelogram
CRhombus
DTrapezoid
Explanation
A quadrilateral with exactly one pair of parallel sides is a trapezoid. AB ∥ DC but AB ≠ DC (16 ≠ 22), confirming it is a trapezoid, not a parallelogram.