Answer: Archimedes go to sleep at 8.32 metres away from the rock.
Step-by-step explanation:
Given that the rock beside which he slept was 5 meters tall
Height h = 5m
Angle Ø = 31 degree
To get distance x away from the rock, we will use trigonometry function. SohCahToa
TanØ = opposite/adjacent
Tan 31 = 5/x
x = 5/tan31
x = 8.32m
Based on the properties of similar triangles, the two true statements are:
- ΔAXC ≅ ΔCXB.
- ΔACB ≅ ΔAXC.
<h3>The properties of similar triangles.</h3>
In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the properties of similar triangles, we have the following points:
- ∠A in ΔAXC matches ∠A in ΔABC and ∠C in ΔCXB.
- ∠C in ΔAXC matches ∠B in ΔABC and ∠B in ΔCXB.
- ∠X in ΔAXC matches ∠C in ΔABC and ∠X in ΔCXB.
In this scenario, we can can logically deduce that the two true statements are:
- ΔAXC is congruent to ΔCXB (ΔAXC ≅ ΔCXB).
- ΔACB is congruent to ΔAXC (ΔACB ≅ ΔAXC).
Read more on similar triangles here: brainly.com/question/7411945
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Answer:
6
Step-by-step explanation:
The 40 feet of fencing which covers at least 182 square feet gives the possible lengths of x as x ≥ 13 or x ≤ 7
<h3>How can the area be expressed as an inequality?</h3>
Length of the fencing = 40 feet
Number of sides covered = Three sides
Area of the fencing ≥ 182 square feet
Length of the shorter side of the pen = x
The area is therefore;
2•x² - 40•x + 182 ≥ 0
2•(x² - 20•x + 91) ≥ 0
2•(x² - 13•x - 7•x + 91) ≥ 0
2•(x•(x - 13) - 7•(x - 13) ≥ 0
Which gives;
The solution to the inequality and the possible lengths of <em>x </em>are;<em> </em>x ≥ 13 or x ≤ 7
Learn more about quadratic inequalities here;
brainly.com/question/10441997
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