### Right Triangle ABCIn this diagram, we have a right triangle labeled as ABC. Here are the key features and measurements of the triangle:- **Vertices**: The triangle has three vertices labeled A, B, and C. The right angle is at vertex B.- **Sides**: - **AB**: This is one of the legs of the triangle and is perpendicular to side BC. - **BC**: This is the other leg of the triangle and is horizontal. - **AC**: This is the hypotenuse of the triangle, opposite the right angle. ### Measurements:- **Side BC (Base)**: The length of side BC, which is the horizontal leg of the triangle, is given as 24 units.- **Side AC (Hypotenuse)**: The length of the hypotenuse AC is given as 25 units.### Right Angle Identification:- The right angle is marked at vertex B, denoted by a small square symbol.This diagram is a classic depiction of a right triangle and can be used to study the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (AB and BC). For this triangle, the relation can be represented as:\[ AB^2 + BC^2 = AC^2 \]Given the lengths, you can verify this as:\[ AB^2 + 24^2 = 25^2 \]This is a fundamental concept in geometry and is widely applicable in various fields of study. **Question:**What is the measure of Angle A? (Round to the nearest tenth)

Hint: Use trigonometric ratio for angle A, P=perpendicular = 24 H=hypotenuse= 25 sinA=P/H

Answered: What is the measure of Angle A? (Round…

Math

Geometry

What is the measure of Angle A? (Round to the nearest tenth)

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter83: Location Of Points

Section: Chapter Questions

Problem 6A: Find the size of A to the nearest second?

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

### Right Triangle ABC

In this diagram, we have a right triangle labeled as ABC. Here are the key features and measurements of the triangle:

- **Vertices**: The triangle has three vertices labeled A, B, and C. The right angle is at vertex B.
- **Sides**:
- **AB**: This is one of the legs of the triangle and is perpendicular to side BC.
- **BC**: This is the other leg of the triangle and is horizontal.
- **AC**: This is the hypotenuse of the triangle, opposite the right angle.

### Measurements:
- **Side BC (Base)**: The length of side BC, which is the horizontal leg of the triangle, is given as 24 units.
- **Side AC (Hypotenuse)**: The length of the hypotenuse AC is given as 25 units.

### Right Angle Identification:
- The right angle is marked at vertex B, denoted by a small square symbol.

This diagram is a classic depiction of a right triangle and can be used to study the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (AB and BC). For this triangle, the relation can be represented as:

\[ AB^2 + BC^2 = AC^2 \]

Given the lengths, you can verify this as:
\[ AB^2 + 24^2 = 25^2 \]

This is a fundamental concept in geometry and is widely applicable in various fields of study.

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