Answer:
Step-by-step explanation:
This question is asking us to find where sin(2x + 30) has a sin of 1. If you look at the unit circle, 90 degrees has a sin of 1. Mathematically, it will be solved like this (begin by taking the inverse sin of both sides):
![sin^{-1}[sin(2x+30)]=sin^{-1}(1)](https://tex.z-dn.net/?f=sin%5E%7B-1%7D%5Bsin%282x%2B30%29%5D%3Dsin%5E%7B-1%7D%281%29)
On the left, the inverse sin "undoes" or cancels the sin, leaving us with
2x + 30 = sin⁻¹(1)
The right side is asking us what angle has a sin of 1, which is 90. Sub that into the right side:
2x + 30 = 90 and
2x = 60 so
x = 30
You're welcome!
Use the sine theorem:
sin(angle A) / length of side a = sin (angle B) / lenght of side b
Here:
angle A = 32°
length of side a = length from school to library = x
angle B = 110°
length of side b = 2.2 mi
Then, sin(32°) / x = sin(110°) / 2.2 mi
=> x = 2.2 mi * sin (32) / sin (110)
x = 1.24 mi
Therefore the answer is the option B. 1.2 mi
4 x 10*5 (the 5 is on top of the 5 but small)