A radio tower is 200 feet tall. How far is an observer from the base of the tower if the angle of
their line of sight hrom the ground to the top of the tower is ? Round to the nearest
hundredth. (t point)

Question

A radio tower is 200 feet tall. How far is an observer from the base of the tower if the angle of
their line of sight hrom the ground to the top of the tower is

? Round to the nearest
hundredth. (t point)

UpStudy AI · Accepted Answer

To determine how far the observer is from the base of the 200-foot-tall radio tower with an angle of elevation of $$ 65^{\circ} $$, we can use trigonometry, specifically the tangent function.

**Step-by-Step Solution:**

1. **Understand the Right Triangle:**
   - **Opposite Side (Height of the Tower):** 200 feet
   - **Angle of Elevation:** $$ 65^{\circ} $$
   - **Adjacent Side (Distance from Observer to Base):** $$ x $$ (what we're trying to find)

2. **Use the Tangent Function:**
   $$
   \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}
   $$
   Plugging in the known values:
   $$
   \tan(65^{\circ}) = \frac{200}{x}
   $$

3. **Solve for $$ x $$:**
   $$
   x = \frac{200}{\tan(65^{\circ})}
   $$

4. **Calculate $$ \tan(65^{\circ}) $$:**
   $$
   \tan(65^{\circ}) \approx 2.1445
   $$

5. **Compute the Distance:**
   $$
   x \approx \frac{200}{2.1445} \approx 93.17 \text{ feet}
   $$

**Final Answer:**
The observer is approximately **93.17 feet** from the base of the tower.
The observer is approximately 93.17 feet from the base of the tower.

A radio tower is 200 feet tall. How far is an observer from the base of the tower if the angle of
their line of sight hrom the ground to the top of the tower is ? Round to the nearest
hundredth. (t point)

Upstudy AI Solution

Answer

Solution

Beyond the Answer

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A radio tower is 200 feet tall. How far is an observer from the base of the tower if the angle of their line of sight hrom the ground to the top of the tower is ? Round to the nearest hundredth. (t point)

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Answer

Solution

Beyond the Answer

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Latest Trigonometry Questions

A radio tower is 200 feet tall. How far is an observer from the base of the tower if the angle of
their line of sight hrom the ground to the top of the tower is ? Round to the nearest
hundredth. (t point)