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Trigonometry
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India
Class X

Side lengths with exact values

Lesson
Practice
Lesson

Worked Examples

Question 1

Find the length of side $h$h.

A right-angled triangle, ABC, has its right angle at vertex B. The other two interior angles are angle C that measures degrees(60) and angle A that measures degrees(30). Side interval(AB) that measures $\sqrt{3}$√3 units is opposite to angle C and adjacent to angle A. Side interval(BC) that measures $h$h units is opposite to angle A and adjacent to angle C. Side interval(AC) is the hypotenuse with a hash mark but is not labeled.

Question 2

Consider the adjacent figure:

  1. Solve for the unknown $\theta$θ. Leave your answer in degrees.

Question 3

Consider the adjacent figure:

A right-angled triangle is depicted with a 45-degree angle at the top. The side opposite the 45-degree angle, and also the base of the triangle, is labeled $y$y. The hypotenuse, extending from the lower right vertex to the upper left vertex, is labeled $x$x.  The side adjacent to the 45-degree angle, and also the height of the triangle, is labeled with the radical expression '4(Square Root of 3)'. The right angle is at the lower left corner of the triangle.

 

  1. Solve for the exact value of $x$x.

  2. Solve for the exact value of $y$y.

Question 4

Consider the equilateral with side lengths of $2$2 units.

  1. Find the perpendicular height $h$h of the triangle.

  2. Determine the measure of angle $x$x.

  3. Determine the exact value of $\sin60^\circ$sin60°.

  4. Determine the exact value of $\cos60^\circ$cos60°.

  5. Determine the exact value of $\tan60^\circ$tan60°.

  6. Determine the exact value of $\sin30^\circ$sin30°.

  7. Determine the exact value of $\cos30^\circ$cos30°.

Outcomes

10.T.IT.1

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined); motivate the ratios, whichever are defined at 0° and 90°. Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°. Relationships between the ratios.

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