https://file.aiquickdraw.com/mathbot/file/1727086003276iylqvgyw.jpg

The image you uploaded contains a right triangle with angle measurements, side lengths, and a prompt asking to "Find *h* as indicated in the figure." From the diagram:

- One of the angles is \( 53.1^\circ \) (an acute angle), and the other acute angle is \( 36.9^\circ \).
- The length of the side adjacent to the \( 53.1^\circ \) angle is labeled as 160 m.
- We are tasked with finding the length of the opposite side, labeled \( h \).

### Solving for \( h \):

To find \( h \), we can use the trigonometric relationship involving the tangent function, which relates the opposite and adjacent sides of a right triangle:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

For this case:
\[
\tan(53.1^\circ) = \frac{h}{160}
\]

Now, solving for \( h \):

\[
h = 160 \times \tan(53.1^\circ)
\]

Let me calculate this.The height \( h \), as indicated in the figure, is approximately 213.1 meters.

Would you like a detailed explanation of how the trigonometric function was applied, or do you have any questions?

Here are five related questions to expand on this concept:
1. How do you calculate the other side of the triangle using the Pythagorean theorem?
2. How would the result change if the angle was larger, like 60° instead of 53.1°?
3. How can we apply the sine or cosine functions to solve for other sides of the triangle?
4. What is the relationship between the angles and the ratios of the sides in a right triangle?
5. Can this approach be applied to non-right triangles? If so, how?

**Tip:** When using trigonometric functions, always make sure your calculator is set to the correct mode (degrees or radians) based on the problem!

A ship leaves a pier and continues on a bearing of N36.9°E, traveling for 160 meters, forming a right triangle. Find the height h indicated in the figure.

Learn how to find the height of a right triangle using trigonometric principles. In this problem, we calculate the height based on a known angle and side length. Suitable for students in Grades 9-11, this solution involves the use of the tangent function.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation