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Key Stage 4

Side lengths with Exact Values

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:

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.

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

Question 4

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

Find the perpendicular height $h$h of the triangle.
Determine the measure of angle $x$x.
Determine the exact value of $\sin60^\circ$sin60°.
Determine the exact value of $\cos60^\circ$cos60°.
Determine the exact value of $\tan60^\circ$tan60°.
Determine the exact value of $\sin30^\circ$sin30°.
Determine the exact value of $\cos30^\circ$cos30°.

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