"[Pic] This arch is formed by an arc..." was answered by our experts

floymdiT

Answered question

2020-11-11

[Pic] This arch is formed by an arc of a circle. What is the radius of the circle?
A. 1.500 m
B. 1.875 m
C. 3.000 m
D. 3.750 m

tafzijdeq

Skilled2020-11-12Added 92 answers

Let r be the radius of the circle so that we can form the diagram as shown containing right triangles:
By the Pythagorean Theorem,

(1.500) 2 + (r - 0.750) 2 = r^{2}

Solve for r. Expand both sides:

2.250 + (r^{2} - 1.500 r + 0.5625) = r^{2}

r^{2} - 1.500 r + 2.8125 = r^{2}

−1.500r+2.8125=0
−1.500r=−2.8125

r = - \frac{2.8125}{- 1.500}

r=1.875m
So, the answer is choice B.

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