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New Zealand
Level 7 - NCEA Level 2

Side lengths with Exact Values

Lesson

Worked Examples

Question 1

Find the length of side $h$h.

A right-angled triangle, $ABC$ABC, is illustrated where a small square placed at vertex $B$B to indicate the right angle. The other two interior angles are angle $C$C that measures $60^\circ$60° and angle $A$A that measures $30^\circ$30°. Side $AB$AB is opposite of angle $C$C. Side $AB$AB is adjacent to angle $A$A. Side $AB$AB measures $\sqrt{3}$3 units. Side $BC$BC is opposite of angle $A$A. Side $BC$BC is adjacent to angle $C$C. Side $BC$BC measures $h$h units. Side $AC$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

M7-4

Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions

91259

Apply trigonometric relationships in solving problems

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