Question

On Planet X, a robotic probe deploys an iron rod to stabilize against a towering alien tree. The rod makes an angle A with the planet's flat surface, where tan A = 60/11. The height of the tree is exactly 120 meters, as scanned by the probe. Find the horizontal distance between the base of the rod and the base of the alien tree.

• A. 33 m
• B. 11 m
• C. 22 m
• D. 44 m

Answer 1

Answer: (C)

22 m

Answer 2

The problem can be modeled as a right-angled triangle.

Let:

• $H$ = Height of the tree = 120 meters
• $X$ = Horizontal distance between the base of the rod and the base of the tree (what we need to find)
• $\tan A = \frac{60}{11}$

Since $\tan A = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{H}{X}$, we have:

$\frac{60}{11} = \frac{120}{X}$

Cross-multiplying:

$60 \times X = 120 \times 11$

Dividing both sides by 60:

$X = \frac{120 \times 11}{60} = 2 \times 11 = 22 \text{ meters}$

Therefore, the horizontal distance is 22 meters.