Let's go through each question step by step:
Question 1:
Given that \(CH = 42\) m and \(CF = 58\) m, we note that \(C\) is the center and \(H\) and \(F\) are points on the circumference. The segment \(HF\) is the chord.
The length of \(FG\) can be found using the properties of circles. However, if we apply the triangle inequality or any specific relationships between segments on circles, we require more clarity about the situation or more angle details. Thus, we need to rely on available options and typical relations in the circular setting usually apply here—assuming standard situations with chords,
Most likely answer is: 40 m.
Question 2:
You can use the Pythagorean theorem or triangle properties to determine the length AO.
Given:
- \(BO = 45\) in.
- \(BA = 108\) in.
We can't express \(AO\) directly without more information, but we can guess based on the scenario. Alternately assuming \(AO^2 + BO^2 = BA^2\)
Using that: \[ AO^2 + 45^2 = 108^2 \implies AO^2 + 2025 = 11664 \implies AO^2 = 9641 \implies AO \approx 98 \text{ inches} \]
So the answer is: 98 in.
Question 3:
For a cyclic quadrilateral \(ABCD\), the following formula applies (using the angles measured in arcs):
- \(m∠A + m∠C = 180°\)
- \(m∠B + m∠D = 180°\)
Given:
- \(m∠B = 93°\)
- Measure of arc \(BC = 58°\)
- Measure of arc \(CD = 106°\)
From the arc measures:
- Angle \(D\) can be calculated as \(180° - (m∠C) = arcCD/2 = 53°\) (simplifying angles based on arc/distribution).
Thus:
- Use supplementary angle concepts \(m∠A + 93° = 180°\) gives \(m∠A = 87°\) considering angles across the cyclic relationship gets rounded near arc totals.
Final answer for measure of \(A\): 82°.
Question 4:
To find the length of the arc, use the formula: \[ \text{Arc Length} = \frac{\theta}{360°} \times 2\pi r \] where \( \theta = 125°\) and \( r = 27 \text{ mm}\).
\[ \text{Arc Length} = \frac{125}{360} \times 2\pi \times 27 = \frac{125 \times 54 \pi}{360} = \frac{6750\pi}{360} = \frac{225\pi}{12} = 75\frac{\pi}{4} \text{ mm} \]
Thus, the answer is: \(75\frac{\pi}{4}\) mm.
Question 5:
To find the area of a sector of a circle, use the formula: \[ \text{Area} = \frac{\theta}{360°} \times \pi r^2 \] where \( \theta = 216°\) and \( r = 7 \text{ inches} \).
\[ \text{Area} = \frac{216}{360} \times \pi (7^2) = \frac{3}{5} \times \pi (49) = \frac{147\pi}{5} \] Calculating \(\frac{147\pi}{5} \approx 29.4 \text{ inches}\).
Thus, the answer is: 29.4 inches.
To summarize:
- 40 m
- 98 in
- 82°
- \(75\frac{\pi}{4}\) mm
- 29.4 inches
1 answer