https://file.aiquickdraw.com/mathbot/file/1730689977625gsiq7kz5.jpg

To solve for \( h \) in the triangle shown, we can use trigonometric relationships. Here's a breakdown of the steps to find \( h \).

### Step 1: Identify Relevant Information
We have:
- Angle \( \angle A = 11^\circ \)
- Angle \( \angle B = 64^\circ \)
- Length \( AB = 376 \)
- Right angle at \( \angle CDB \)

### Step 2: Use Trigonometry to Find \( h \)
Since \( h \) is opposite to angle \( B = 64^\circ \), we can use the sine function in the right triangle \( \triangle BCD \) to find \( h \):

\[
\sin(64^\circ) = \frac{h}{AB}
\]

Rearranging to solve for \( h \):

\[
h = AB \cdot \sin(64^\circ)
\]

### Step 3: Substitute Values and Calculate
1. Substitute \( AB = 376 \) and \( \sin(64^\circ) \approx 0.8988 \) (using a calculator or table for trigonometric values):
   \[
   h = 376 \cdot 0.8988
   \]

2. Calculate:
   \[
   h \approx 338.5
   \]

### Answer
The length of \( h \) is approximately **338.5** units when rounded to the nearest tenth.

---

Would you like further clarification or have additional questions?

### Additional Questions
1. How do trigonometric ratios change based on the angles in a triangle?
2. What other methods could be used to solve for side lengths in a right triangle?
3. Why is the sine function suitable for finding \( h \) in this scenario?
4. How would the solution change if angle \( B \) were different?
5. What tools can be used to approximate trigonometric values accurately?

### Tip
When working with trigonometric functions, always make sure your calculator is set to the correct mode (degrees or radians) based on the angle unit you are using.

Find h to the nearest tenth. Given triangle ABC with angle A = 11°, angle B = 64°, AB = 376 units, and right angle at D.

Learn how to find the length of side h in a right triangle with given angles and side length. This example demonstrates using the sine function to calculate the opposite side when the hypotenuse and angle are known. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation