https://file.aiquickdraw.com/mathbot/file/1727434777454ssvl086i.jpg

Let's solve the questions one by one:

### (a) Lower Bound for the Lengths of \( AB \) and \( BC \)

1. **(i) Lower bound for \( AB \):**

   The length \( AB = 20 \) cm, correct to 1 significant figure. The lower bound is calculated as:
   \[
   \text{Lower bound} = 20 - 0.5 = 19.5 \text{ cm}
   \]

2. **(ii) Lower bound for \( BC \):**

   The length \( BC = 8.3 \) cm, correct to 2 significant figures. The lower bound is calculated as:
   \[
   \text{Lower bound} = 8.3 - 0.05 = 8.25 \text{ cm}
   \]

### (b) Lower Bound for the Area of Triangle \( ABC \)

The area of a right-angled triangle is given by:
\[
\text{Area} = \frac{1}{2} \times AB \times BC
\]
Using the lower bounds:
\[
\text{Lower bound of Area} = \frac{1}{2} \times 19.5 \times 8.25 = 80.4375 \text{ cm}^2
\]

### (c) Lower Bound for the Value of \( \tan x^\circ \)

The tangent of angle \( x^\circ \) is given by:
\[
\tan x^\circ = \frac{BC}{AB}
\]
Using the lower bounds:
\[
\text{Lower bound of } \tan x^\circ = \frac{8.25}{20.5} \approx 0.4024
\]

These are the calculated lower bounds. Let me know if you would like to see more details or have any questions about this solution!

### 5 Relative Questions:
1. What is the upper bound for the length of \( AB \) and \( BC \)?
2. How does changing the number of significant figures affect the lower bound calculation?
3. How would you find the upper bound of the area of triangle \( ABC \)?
4. How can we verify the calculated lower bounds using the concept of error intervals?
5. How would the lower bound of \( \tan x^\circ \) change if \( AB \) had 2 significant figures?

### Tip:
When dealing with measurements and bounds, always keep track of the precision and significant figures to ensure accurate calculations.

Write down the lower bound for the lengths of AB and BC, calculate the lower bound for the area of triangle ABC, and calculate the lower bound for the value of tan x°.

Explore how to calculate the lower bounds for the lengths of AB and BC, the area of a right-angled triangle ABC, and the value of tan x° based on provided measurements. The question delves into measurement precision, geometric area calculations, and trigonometry, suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation