**Title: Solving for an Angle in a Right Triangle****Objective:** Learn how to determine the measure of an angle in a right-angled triangle using the given lengths of the hypotenuse and one adjacent side.### Problem Statement**Solve for $ x $. Round to the nearest tenth of a degree, if necessary.**### Given Diagram:A right-angled triangle $ \triangle KLM $ is presented with the following details:- Segment $ KM $ is the hypotenuse, labeled with a length of $ 6.5 $ units.- Segment $ LM $ is one of the legs (adjacent to angle $ x^\circ $), labeled with a length of $ 4.4 $ units.- The right angle is located at vertex $ L $.### Solution ApproachTo find the angle $ x $:1. **Trigonometric Ratio**: Use the cosine function, which relates the adjacent side and the hypotenuse in a right-angled triangle. \[ \cos(x) = \frac{\text{adjacent side}}{\text{hypotenuse}} \] For $ \triangle KLM $: \[ \cos(x) = \frac{LM}{KM} = \frac{4.4}{6.5} \]2. **Calculate the Cosine Value**: \[ \cos(x) = \frac{4.4}{6.5} \approx 0.6769 \]3. **Determine the Angle**: Use the inverse cosine function (often denoted as $ \cos^{-1} $ or $ \text{arccos} $) to find the angle: \[ x = \cos^{-1}(0.6769) \]4. **Use a Calculator to Find $ x $**: \[ x \approx 47.1^\circ \]### ConclusionThe value of $ x $ is approximately $ 47.1 $ degrees when rounded to the nearest tenth of a degree.**Note:** Ensure the calculator is set to degree mode to get the correct measure of the angle in degrees.

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Answered: Solve for a. Round to the nearest tenth…

Math

Geometry

Solve for a. Round to the nearest tenth of a degree, if necessary. K. 6.5 L. M. 4.4

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter1: Variables, Expressions, And Integers

Section1.8: The Coordinate Plane

Problem 2E

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Question

**Title: Solving for an Angle in a Right Triangle**

**Objective:** Learn how to determine the measure of an angle in a right-angled triangle using the given lengths of the hypotenuse and one adjacent side.

### Problem Statement
**Solve for $ x $. Round to the nearest tenth of a degree, if necessary.**

### Given Diagram:
A right-angled triangle $ \triangle KLM $ is presented with the following details:
- Segment $ KM $ is the hypotenuse, labeled with a length of $ 6.5 $ units.
- Segment $ LM $ is one of the legs (adjacent to angle $ x^\circ $), labeled with a length of $ 4.4 $ units.
- The right angle is located at vertex $ L $.

### Solution Approach
To find the angle $ x $:

1. **Trigonometric Ratio**: Use the cosine function, which relates the adjacent side and the hypotenuse in a right-angled triangle.
\[
\cos(x) = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]
For $ \triangle KLM $:
\[
\cos(x) = \frac{LM}{KM} = \frac{4.4}{6.5}
\]

2. **Calculate the Cosine Value**:
\[
\cos(x) = \frac{4.4}{6.5} \approx 0.6769
\]

3. **Determine the Angle**: Use the inverse cosine function (often denoted as $ \cos^{-1} $ or $ \text{arccos} $) to find the angle:
\[
x = \cos^{-1}(0.6769)
\]

4. **Use a Calculator to Find $ x $**:
\[
x \approx 47.1^\circ
\]

### Conclusion
The value of $ x $ is approximately $ 47.1 $ degrees when rounded to the nearest tenth of a degree.

**Note:** Ensure the calculator is set to degree mode to get the correct measure of the angle in degrees.

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