A boat is 375 teet from the base of a cillt. Andrew, whe is at the top of the eillt, noticea that the angle ef depreasien to the
boat is 64 . How high is the cilfre Round to the nearest tenth.
642.7 teet
417.2 teet
182.9 teet
768.9 teet

Question

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### **Problem Statement:**
A boat is **375 feet** from the base of a **cliff**. Andrew, who is at the top of the **cliff**, notices that the **angle of depression** to the boat is **64 degrees**. How high is the cliff? **Round to the nearest tenth**.

**Options:**
- 642.7 feet
- 417.2 feet
- 182.9 feet
- 768.9 feet

### **Understanding the Problem:**
- **Angle of Depression:** The angle formed by the line of sight when looking downward from a horizontal line.
- **Given:**
  - Distance from the boat to the base of the cliff (horizontal distance): **375 feet**
  - Angle of depression: **64°**
- **Find:** Height of the cliff (**h**)

### **Diagram:**
Imagine a right triangle where:
- The **horizontal side** (adjacent to the angle) is **375 feet**.
- The **vertical side** (opposite to the angle) is the height of the cliff (**h**) we need to find.
- The **angle** at the top of the cliff is **64°**.

### **Trigonometric Relationship:**
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

$$
\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}
$$

Plugging in the known values:

$$
\tan(64°) = \frac{h}{375}
$$

### **Solving for Height (h):**

1. **Calculate $$\tan(64°)$$:**
   $$
   \tan(64°) \approx 2.0503
   $$

2. **Multiply both sides by 375 to solve for $$h$$:**
   $$
   h = 375 \times \tan(64°) \
   h \approx 375 \times 2.0503 \
   h \approx 768.8625 \text{ feet}
   $$

3. **Round to the nearest tenth:**
   $$
   h \approx 768.9 \text{ feet}
   $$

### **Answer:**
**768.9 feet**
The height of the cliff is approximately **768.9 feet**.

A boat is 375 teet from the base of a cillt. Andrew, whe is at the top of the eillt, noticea that the angle ef depreasien to the
boat is 64 . How high is the cilfre Round to the nearest tenth.
642.7 teet
417.2 teet
182.9 teet
768.9 teet

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A boat is 375 teet from the base of a cillt. Andrew, whe is at the top of the eillt, noticea that the angle ef depreasien to the boat is 64 . How high is the cilfre Round to the nearest tenth. 642.7 teet 417.2 teet 182.9 teet 768.9 teet

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Trigonometry Questions

A boat is 375 teet from the base of a cillt. Andrew, whe is at the top of the eillt, noticea that the angle ef depreasien to the
boat is 64 . How high is the cilfre Round to the nearest tenth.
642.7 teet
417.2 teet
182.9 teet
768.9 teet