Construct a triangle ABC of side ab= 3 cm,ac=5 and Angle BAC is 90°

To construct a triangle ABC where side \( AB = 3 \, \text{cm} \), side \( AC = 5 \, \text{cm} \), and \( \angle BAC = 90^\circ \), follow these steps:

### Steps for Construction:
1. **Draw Line Segment AB**:  
   Draw a horizontal line segment \( AB = 3 \, \text{cm} \).

2. **Construct a \( 90^\circ \) Angle at Point A**:  
   At point \( A \), use a protractor to construct a \( 90^\circ \) angle. This means the line will be perpendicular to line \( AB \).

3. **Mark Point C on the Perpendicular Line**:  
   From point \( A \), measure a distance of \( AC = 5 \, \text{cm} \) along the perpendicular line. Mark this point as \( C \).

4. **Connect Point C to Point B**:  
   Draw a line connecting \( C \) to \( B \). Now you have your required triangle \( \triangle ABC \).

### Verifying the Triangle:
This triangle is a right triangle with \( \angle BAC = 90^\circ \). By the Pythagorean theorem, check if:
\[
AB^2 + AC^2 = BC^2
\]
\[
3^2 + 5^2 = BC^2 \quad \text{or} \quad 9 + 25 = 34
\]
Thus, \( BC = \sqrt{34} \approx 5.83 \, \text{cm} \).

Would you like more details, or do you have any questions?

---

Here are 5 related questions to explore:
1. How do you verify the angle in triangle constructions?
2. Can you construct a triangle given three sides (SSS criterion)?
3. How do you apply the Pythagorean theorem to other right triangles?
4. What is the general formula for calculating the area of a right triangle?
5. How would you construct a triangle given one angle and two sides not including that angle?

**Tip**: Always ensure the accuracy of your angle constructions using a protractor to maintain geometric precision.

Construct a triangle ABC of side ab= 3 cm, ac= 5 cm, and Angle BAC is 90°

Learn how to construct a right triangle with side AB = 3 cm, side AC = 5 cm, and a right angle at BAC (90°). This step-by-step guide explains the geometric construction process and verifies the solution using the Pythagorean theorem. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation