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Class 824 Class 924 Class 1036

SubjectAll Physics 19 Chemistry 19 Biology 19 Mathematics 27

ChapterAll Arithmetic Progressions Circles Coordinate Geometry Introduction to Trigonometry Pair of Linear Equations in Two Variables Polynomials Probability Quadratic Equations Real Numbers Some Applications of Trigonometry Statistics Surface Areas and Volumes Triangles

Showing 1 question in Mathematics for Class 10. Tap a card to reveal the answer.

MathematicsSome Applications of Trigonometrymedium

The angle of elevation of the top of a tower from a point 30 m from its base is 30 degrees. Find the height of the tower.

Reveal answer ↓

What it is

An angle of elevation turns a triangle into a height problem using tan = opposite / adjacent.

Answer

Let the height be h. tan(30 degrees) = h / 30, and tan(30 degrees) = 1/sqrt(3). So h = 30 x (1/sqrt(3)) = 30/sqrt(3) = 10 sqrt(3) m, which is about 17.3 m.

tan(theta) = height / base distance

•tan(angle) = opposite/adjacent = h/30
•tan(30 deg) = 1/sqrt(3)
•h = 10 sqrt(3) m (about 17.3 m)

Why learn this

Surveyors, pilots and builders measure unreachable heights (towers, hills) exactly this way.

💡 Memory trick

Draw the right triangle; tan(angle) = height / base distance.