Question

answer the following question using the measurements of the right triangle in your home from the beginning of the lesson. draw a sketch of the right triangle - shaped item in your home, and label each side length with your calculated measurement.

Explanation:

To complete this task, you can follow these steps:

Step 1: Identify a right - triangle - shaped item at home

For example, a right - angled corner of a bookshelf, a triangular - shaped ruler (if it's a right - triangle), or the frame of a right - triangle - shaped photo frame. Let's take a right - triangle - shaped keychain as an example.

Step 2: Measure the sides

1. Measure the legs: Use a ruler to measure the two legs (the sides forming the right angle) of the right - triangle - shaped item. Suppose we measure one leg (let's call it \(a\)) as \(3\) cm and the other leg (let's call it \(b\)) as \(4\) cm.
2. Calculate the hypotenuse: For a right triangle, we can use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse. Substituting \(a = 3\) cm and \(b=4\) cm into the formula, we get \(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25} = 5\) cm.

Step 3: Draw the sketch

• Draw a right - angled triangle.
• Label the two legs with the measured lengths (e.g., one leg as \(3\) cm, the other as \(4\) cm) and the hypotenuse with the calculated length (e.g., \(5\) cm).

If you are using the sketchpad tool:

• Use the pencil tool to draw the triangle.
• Use the text tool (the 'T' icon) to label each side with the appropriate length.

For example, if your right - triangle - shaped item is a small triangular - shaped tile with legs of length \(5\) cm and \(12\) cm:

• Calculate the hypotenuse: \(c=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13\) cm.
• Then draw the triangle and label the sides as \(5\) cm, \(12\) cm, and \(13\) cm.

Answer:

To complete this task, you can follow these steps:

Step 1: Identify a right - triangle - shaped item at home

For example, a right - angled corner of a bookshelf, a triangular - shaped ruler (if it's a right - triangle), or the frame of a right - triangle - shaped photo frame. Let's take a right - triangle - shaped keychain as an example.

Step 2: Measure the sides

1. Measure the legs: Use a ruler to measure the two legs (the sides forming the right angle) of the right - triangle - shaped item. Suppose we measure one leg (let's call it \(a\)) as \(3\) cm and the other leg (let's call it \(b\)) as \(4\) cm.
2. Calculate the hypotenuse: For a right triangle, we can use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse. Substituting \(a = 3\) cm and \(b=4\) cm into the formula, we get \(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25} = 5\) cm.

Step 3: Draw the sketch

• Draw a right - angled triangle.
• Label the two legs with the measured lengths (e.g., one leg as \(3\) cm, the other as \(4\) cm) and the hypotenuse with the calculated length (e.g., \(5\) cm).

If you are using the sketchpad tool:

• Use the pencil tool to draw the triangle.
• Use the text tool (the 'T' icon) to label each side with the appropriate length.

For example, if your right - triangle - shaped item is a small triangular - shaped tile with legs of length \(5\) cm and \(12\) cm:

• Calculate the hypotenuse: \(c=\sqrt{5^{2}+12^{2}}=\sqrt{25 + 144}=\sqrt{169}=13\) cm.
• Then draw the triangle and label the sides as \(5\) cm, \(12\) cm, and \(13\) cm.