Let x be the first of the four consecutive numbers.
Then x+1 is the second,
and x+2 is the third,
and x+3 is the fourth.
If their sum is 810, then
x + x+1 + x+2 + x+3 = 810
If you solve that equation for x, you'll have the answer to your question.
The question is as follow:
<span>Given a possible triangle ABC with a=5, b=11, and A=23 degrees, find a possible value for angle B. Round to the nearest tenth.
A. 10.2° B. 11.2° C. 59.3° D. no solution
</span><span>========================================================
</span>
<span>a = 5 , b = 11 , and ∠A = 23°
</span><span>By applying the Law of Sines:
![\frac{sin \ A}{a} = \frac{sin \ B}{b}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%20%5C%20A%7D%7Ba%7D%20%3D%20%5Cfrac%7Bsin%20%5C%20B%7D%7Bb%7D%20)
</span>
<span>
![\frac{sin \ 23}{5} = \frac{sin \ B}{11}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%20%5C%2023%7D%7B5%7D%20%3D%20%5Cfrac%7Bsin%20%5C%20B%7D%7B11%7D%20)
∴ sin B = 11* (sin 23°)/5 ≈ 0.8596
∴ ∠B =
![sin^{-1} 0.8596](https://tex.z-dn.net/?f=%20sin%5E%7B-1%7D%200.8596%20)
≈ 59.3°
∴ The correct choice is option (C)</span>
<span> C. 59.3°</span>
Answer:
![\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}](https://tex.z-dn.net/?f=%5Chuge%5Cunderline%7B%5Cred%7BA%7D%5Cblue%7Bn%7D%5Cpink%7Bs%7D%5Cpurple%7Bw%7D%5Corange%7Be%7D%5Cgreen%7Br%7D%20-%7D)
<u>Circumference</u><u> </u><u>of </u><u>a </u><u>circle </u><u>is </u><u>given </u><u>by </u>
<u>
</u>
- Given - <u>Diameter</u><u> </u><u>of </u><u>circle </u><u>=</u><u> </u><u>1</u><u>0</u><u> </u><u>yards</u>
![radius = \frac{diameter}{2} = \frac{10}{2} \\ \\ \implies \: 5 \: yards](https://tex.z-dn.net/?f=radius%20%3D%20%20%5Cfrac%7Bdiameter%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B10%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%5Cimplies%20%5C%3A%205%20%5C%3A%20yards)
now ,
<u>substituting</u><u> </u><u>the </u><u>value </u><u>of </u><u>r </u><u>in </u><u>the </u><u>formula </u><u>of </u><u>circumference</u><u> </u><u>~</u>
![C = 2 \times \frac{22}{7} \times 5 \\ \\ \implies \: C = \frac{220}{7} \\ \\ \implies \: C = 31.43 \: yards \: (approx.)](https://tex.z-dn.net/?f=C%20%3D%20%202%20%5Ctimes%20%20%5Cfrac%7B22%7D%7B7%7D%20%20%20%5Ctimes%205%20%5C%5C%20%20%5C%5C%20%5Cimplies%20%5C%3A%20C%20%3D%20%20%5Cfrac%7B220%7D%7B7%7D%20%20%5C%5C%20%20%5C%5C%20%5Cimplies%20%5C%3A%20C%20%3D%2031.43%20%5C%3A%20yards%20%5C%3A%20%28approx.%29)
hope helpful :D
Where is the point t in question