Subscribe

9th grade · Math · Unit 8 of 18

Right-Triangle Trig

Sine, cosine and tangent

What your child practices

The three trig ratios in a right triangle (SOH CAH TOA), choosing the right ratio for the sides you know, finding a missing side, and seeing why sin A = cos B for the two acute angles.

Alabama Course of Study content standard: GDA.35 · sine, cosine and tangent in right triangles and using them to find missing sides

How we explain it

Children can open this short lesson before they practice.

  1. Name the sides from angle A: opposite, adjacent (next to A) and the hypotenuse (across from the right angle).
  2. SOH CAH TOA: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
  3. Pick the ratio that uses the side you know and the side you want, then solve.

Example: sin A = 0.6 and the hypotenuse is 20 cm. How long is the side opposite A? sin A = opposite ÷ hypotenuse. opposite = 0.6 × 20. Answer: 12 cm

Right-Triangle Trig in Alabama

In the Alabama Course of Study, this is unit 8 of 18 in 9th grade Math, after Right Triangles & Scaling and before Circle Properties.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alabama State Department of Education (ALSDE)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    You know angle A and the hypotenuse of a right triangle. You want the adjacent side. Which ratio links them?

    • Tangent
    • Sine
    • Cosine

  2. Question 2

    A ramp rises at a 45° angle and runs 7 m along the ground. How high does it rise? (tan 45° = 1)

    • 7
    • 8
    • 14
    • 4

  3. Question 3

    In a right triangle, the side opposite angle A is 8, the side next to angle A is 15 and the hypotenuse is 17. What is cos A?

    • 8/17
    • 15/17
    • 8/15
    • 15/8

  4. Question 4

    For an acute angle A in a right triangle, which ratio is cos A?

    • adjacent ÷ hypotenuse
    • opposite ÷ adjacent
    • opposite ÷ hypotenuse
    • hypotenuse ÷ opposite

  5. Question 5

    In a right triangle, tan A = 0.75 and the side next to angle A is 32 cm. How long is the side opposite angle A?

    • 32
    • 24
    • 35
    • 40

  6. Question 6

    In a right triangle, one acute angle is 13°. What is the other acute angle?

    • 87°
    • 77°
    • 13°
    • 167°

More 9th grade