In the triangle below, ∠A = 55° and ∠B = 65°. What is the measure of ∠C?
A50°
B70°
C60°
D75°
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 2 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?
A18.0 feet
B24.0 feet
C20.0 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 3 of 10
Florida standards 9A-9BMedium Calc Word Diagram
From the top of a lighthouse 90 feet tall, the angle of depression to a boat is 28°. How far is the boat from the base of the lighthouse? (tan 28° ≈ 0.532)
A47.9 feet
B203.4 feet
C169.2 feet
D101.8 feet
Explanation
The angle of depression equals the angle of elevation from the boat. tan(28°) = opposite/adjacent = 90/d d = 90/tan(28°) = 90/0.532 ≈ 169.2 feet.
Question 4 of 10
Florida standards 11A-11DMedium Calc Word Diagram
A swimming pool has the shape shown below — a rectangle with a semicircle on each end. Find the total area of the pool. (Use π ≈ 3.14)
A200.0 m²
B278.5 m²
C257.0 m²
D356.0 m²
Explanation
Rectangle area = 20 × 10 = 200 m². Two semicircles = one full circle with r = 5: π × 5² = 3.14 × 25 = 78.5 m². Total = 200 + 78.5 = 278.5 m².
Question 5 of 10
Florida standards 1A-1GHard Calc Word
A composite figure is made of a rectangle (10 m × 6 m) with a semicircle attached to one of the shorter sides. What is the total area? (Use π ≈ 3.14)
A64.7 m²
B102.5 m²
C88.3 m²
D74.1 m²
Explanation
📌 Step 1: Break into simple shapes Rectangle: 10 m × 6 m Semicircle: radius = 6/2 = 3 m (attached to the 6 m side)
📌 Step 2: Calculate each area Rectangle = 10 × 6 = 60 m² Semicircle = ½πr² = ½ × 3.14 × 3² = ½ × 28.26 = 14.13 m²
📌 Step 3: Add them Total = 60 + 14.13 = 74.13 ≈ 74.1 m²
💡 Strategy for composite figures: Always break them into shapes you know (rectangles, triangles, circles), calculate each, then add (or subtract for holes).
Question 6 of 10
Florida standards 8A-8BHard Calc Word Diagram
In right triangle ABC, an altitude CD is drawn from the right angle C to hypotenuse AB. If AD = 5 and DB = 12, what is the length of CD?
A8.5
B√85 ≈ 9.22
C2√15 ≈ 7.75
D√17 ≈ 4.12
Explanation
The altitude to the hypotenuse is the geometric mean of the two segments: CD = √(AD × DB) = √(5 × 12) = √60 = 2√15 ≈ 7.75.
Question 7 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)
💡 Tip: This is a multiple of the 8-15-17 Pythagorean triple (×5 = 40-75-85).
Question 9 of 10
Florida standards 4A-4DEasy Calc Word Diagram
Jake claims: "If a quadrilateral has four right angles, then it must be a square." Which figure below is a counterexample?
ARhombus
BRectangle
CSquare
DTrapezoid
Explanation
A rectangle has four right angles but is NOT necessarily a square (it can have unequal side lengths). The rectangle with sides 90×60 is a counterexample to Jake's claim.
Question 10 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?
A10
B8
C12
D14
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.