Geometry and TrigonometryVery hardHeight of a tower from two angles of elevation
Geometry and Trigonometry practice question
From a point on level ground, the angle of elevation to the top of a tower is 30°. From a point 40 metres closer to the tower, on the same line, the angle of elevation is 60°. What is the height of the tower, rounded to the nearest metre?
Answer: 35
With height h and nearer distance d, h = d·tan 60° and h = (d + 40)·tan 30°. Solving gives d = 20 and h = 20√3 ≈ 34.6, which rounds to 35.
Common wrong answers
- If you answered 23
- 23 uses 40 tan 30°.
- If you answered 40
- 40 is the distance between the two points.
- If you answered 69
- 69 uses 40 tan 60°.
More Geometry and Trigonometry questions
- Very hard
Two parallel lines are cut by a transversal. One of the eight angles measures 47°. Which of the following is N… - Very hard
In a right triangle, angles A and B are the two acute angles, so A + B = 90°. If sin A = 0.6, what is the valu… - Very hard
A regular hexagon has a side length of 4. What is its area? (A regular hexagon of side s has area (3√3/2)s².) - Very hard
A cone has a radius of 6 and a height of 10. What is its volume? (Use V = (1/3)πr²h.) - Very hard
In the xy-plane, the graph of x² + y² − 12x − 4y + 15 = 0 is a circle. The line 3x − 4y = 25 intersects this c… - Very hard
What is the perimeter of triangle ABC?
Not affiliated with the College Board. SAT is a trademark of the College Board.