Free Year 9 Scientific notation Practice | Skillo

Question 1 — Easy

Anika is a wildlife ranger tracking a koala in a eucalyptus tree. She stands 12 m from the base of the tree on flat ground and measures the angle of elevation to the koala as 53°. Her eyes are 1.6 m above the ground. What is the height of the koala above the ground, correct to the nearest tenth of a metre?

Answer: Using tan(53°) = opposite ÷ adjacent, the vertical distance from Anika's eyes to the koala = 12 × tan(53°) ≈ 12 × 1.3270 ≈ 15.9 m. Adding Anika's eye height of 1.6 m gives total height above ground = 15.9 + 1.6 = 17.5 m. Option A (15.9 m) is the height above Anika's eye level only, omitting the 1.6 m eye height — a common multi-step error. Option C (7.2 m) results from using 12 × tan(31°) ≈ 7.2, applying the complement angle. Option D (20.0 m) results from using 12 ÷ sin(37°) or a similar hypotenuse-based miscalculation.

Question 2 — Medium

A cable anchors a communication tower to the ground. The cable is 18 m long and is attached to the top of the tower. The cable makes an angle of 34° with the vertical tower. Which calculation gives the horizontal distance from the base of the tower to the anchor point, correct to the nearest metre?

Answer: The cable is the hypotenuse (18 m) and the angle is measured from the vertical tower. The horizontal distance is opposite to the 34° angle, so the ratio required is sin(34°) = opposite ÷ hypotenuse, giving 18 × sin(34°) ≈ 10 m. Option B uses cosine, which gives the side adjacent to the angle (the tower height, not the horizontal distance). Option C uses tangent, which applies only when the hypotenuse is not involved. Option D incorrectly divides rather than multiplies, treating the horizontal distance as the hypotenuse.

Question 3 — Hard

A cable is stretched from the top of a 12 m vertical pole to a point on the ground. The cable makes an angle of 35° with the ground. Zac needs to find the length of the cable. Which expression correctly calculates the length of the cable to the nearest metre?

Answer: Option A is correct — The pole is the side opposite the 35° angle, and the cable is the hypotenuse. Using sin(35°) = opposite ÷ hypotenuse gives hypotenuse = 12 ÷ sin(35°) ≈ 20.9 ≈ 21 m. Option B confuses the formula by multiplying instead of dividing.