25 is the answer
23+25+27+29+31
Answer:
A-0.5777miles
B-0.7223miles
Step-by-step explanation:
Let A be truck with 58°, B be truck with 52° elevation and C be the position of the fire. We know that the AB is 1.3 miles apart.
-Using sine rule, we find the length of AB and BC as:
![\angle C=180-(58+52)=70\textdegree\\\\\frac{a}{sin \ A}=\frac{b}{sin \ B}=\frac{c}{sin \ C}\\\\\frac{1.3}{sin \ 70}=\frac{b}{sin \ 52}\\\\b=\frac{1.3 sin \ 52}{sin 70}=1.0902mi\\\\\\c=\frac{1.3 sin \ 58}{sin 70}=1.1732](https://tex.z-dn.net/?f=%5Cangle%20C%3D180-%2858%2B52%29%3D70%5Ctextdegree%5C%5C%5C%5C%5Cfrac%7Ba%7D%7Bsin%20%5C%20A%7D%3D%5Cfrac%7Bb%7D%7Bsin%20%5C%20B%7D%3D%5Cfrac%7Bc%7D%7Bsin%20%5C%20C%7D%5C%5C%5C%5C%5Cfrac%7B1.3%7D%7Bsin%20%5C%2070%7D%3D%5Cfrac%7Bb%7D%7Bsin%20%5C%2052%7D%5C%5C%5C%5Cb%3D%5Cfrac%7B1.3%20sin%20%5C%2052%7D%7Bsin%2070%7D%3D1.0902mi%5C%5C%5C%5C%5C%5Cc%3D%5Cfrac%7B1.3%20sin%20%5C%2058%7D%7Bsin%2070%7D%3D1.1732)
#Bisect angle C, and use sine rule again to find the lengths of bisected AB:
![\frac{a}{sin \ A}=\frac{b}{sin \ B}=\frac{c}{sin \ C}\\\\\frac{1.0902}{sin \ 90}=\frac{x}{sin \ (90-58)}\\\\x=\frac{1.0902\ sin \ 32}{sin \ 90}=0.5777mi](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%20%5C%20A%7D%3D%5Cfrac%7Bb%7D%7Bsin%20%5C%20B%7D%3D%5Cfrac%7Bc%7D%7Bsin%20%5C%20C%7D%5C%5C%5C%5C%5Cfrac%7B1.0902%7D%7Bsin%20%5C%2090%7D%3D%5Cfrac%7Bx%7D%7Bsin%20%5C%20%2890-58%29%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B1.0902%5C%20sin%20%5C%2032%7D%7Bsin%20%5C%2090%7D%3D0.5777mi)
Truck B's position is calculated as 1.3mi-0.5777miles=0.7223miles
Hence, truck one is 0.5777miles and truck two is 0.7223 miles from the fire.
Answer: 14:3
Step-by-step explanation:
Given
Ratio between students(s) to female(f) adults is 7:6
while ratio between female(f) to male(m) is 4:1
So, we can write
![\Rightarrow \dfrac{s}{f}=\dfrac{7}{6}\quad \ldots(i)](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7Bs%7D%7Bf%7D%3D%5Cdfrac%7B7%7D%7B6%7D%5Cquad%20%5Cldots%28i%29)
Also, we can write
![\Rightarrow \dfrac{f}{m}=\dfrac{4}{1}\quad \ldots(ii)](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7Bf%7D%7Bm%7D%3D%5Cdfrac%7B4%7D%7B1%7D%5Cquad%20%5Cldots%28ii%29)
Multiply both equations
![\Rightarrow \dfrac{s}{f}\times \dfrac{f}{m}=\dfrac{7}{6}\times \dfrac{4}{1}\\\\ \Rightarrow \dfrac{s}{m}=\dfrac{14}{3}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7Bs%7D%7Bf%7D%5Ctimes%20%5Cdfrac%7Bf%7D%7Bm%7D%3D%5Cdfrac%7B7%7D%7B6%7D%5Ctimes%20%5Cdfrac%7B4%7D%7B1%7D%5C%5C%5C%5C%20%5CRightarrow%20%5Cdfrac%7Bs%7D%7Bm%7D%3D%5Cdfrac%7B14%7D%7B3%7D)
So, the ratio of the students to male adults is 14:3 .
Answer:
25°
Step-by-step explanation:
whole angle = 69°
m<1 is 19 more than m <2 then
(69 - 19) ÷ 2 = m<2
m <2 = 25