A kite is flying at the end of a 200-foot string. The string makes a 55° angle with the ground. How high above the ground is the kite? Round to the nearest foot. (sin 55° ≈ 0.819)
A186 feet
B141 feet
C115 feet
D164 feet
Explanation
📌 Step 1: Identify the trig ratio We know the hypotenuse (200 ft) and want the opposite side (height). Use sine: sin = opposite / hypotenuse
📌 Step 2: Set up and solve sin(55°) = h / 200 0.819 = h / 200 h = 200 × 0.819 = 163.8
📌 Answer: ≈ 164 feet
💡 Tip: Angle of elevation from ground = angle between the string and the horizontal, NOT the vertical.
Question 2 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?
A2√15 ≈ 7.75
B√17 ≈ 4.12
C√85 ≈ 9.22
D8.5
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 3 of 10
Florida standards 1A-1GMedium Calc Word Diagram
A zip-line connects the top of a 40-foot platform to a point on the ground 75 feet away. What is the length of the zip-line cable?
A75 feet
B95 feet
C85 feet
D80 feet
Explanation
📌 Step 1: Identify the right triangle The platform height (40 ft), ground distance (75 ft), and cable form a right triangle.
💡 Common mistake: Don't forget to divide by 3! A cone is 1/3 the volume of a cylinder with the same base and height.
Question 6 of 10
Florida standards 1A-1GEasy Calc Word
A pizza box is 14 inches on each side and 2 inches tall. What is the volume of the box?
A448 in³
B392 in³
C280 in³
D196 in³
Explanation
📌 Step 1: Identify the shape A pizza box is a rectangular prism (cuboid).
📌 Step 2: Apply the volume formula V = length × width × height V = 14 × 14 × 2
📌 Step 3: Calculate = 392 in³
💡 Quick check: Volume is always in cubic units. If your answer is in square units, something went wrong!
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?
A22.5 feet
B18.0 feet
C20.0 feet
D24.0 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 7A-7BMedium Calc Word Diagram
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?
A27 feet
B24 feet
C30 feet
D36 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 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
BSquare
CRectangle
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 3A-3DEasy Calc Word Diagram
Which of the following figures has BOTH reflectional and rotational symmetry?
AB (Regular hexagon)
BA (Scalene triangle)
CC (Parallelogram)
DD (Arrow)
Explanation
📌 Step 1: Check each figure
A (Scalene triangle): No lines of symmetry, no rotational symmetry ✗ B (Regular hexagon): 6 lines of symmetry + rotational symmetry at 60° ✓ C (Parallelogram): No lines of symmetry, rotational symmetry at 180° only → partial ✗ D (Arrow): 1 line of symmetry (vertical) but no rotational symmetry ✗
📌 Answer: B (Regular hexagon)
💡 Tip: All regular polygons have BOTH reflectional AND rotational symmetry. The number of symmetry lines = number of sides.