Answer:
Step-by-step explanation:
![\sin \theta+\cot \theta\cos \theta=\sin \theta+\displaystyle \frac{\cos \theta}{\sin \theta}\cos \theta=\frac{\sin^2 \theta+\cos ^2 \theta}{\sin \theta}=\\\frac{1}{\sin \theta}=\csc \theta](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%2B%5Ccot%20%5Ctheta%5Ccos%20%5Ctheta%3D%5Csin%20%5Ctheta%2B%5Cdisplaystyle%20%5Cfrac%7B%5Ccos%20%5Ctheta%7D%7B%5Csin%20%5Ctheta%7D%5Ccos%20%5Ctheta%3D%5Cfrac%7B%5Csin%5E2%20%5Ctheta%2B%5Ccos%20%5E2%20%5Ctheta%7D%7B%5Csin%20%5Ctheta%7D%3D%5C%5C%5Cfrac%7B1%7D%7B%5Csin%20%5Ctheta%7D%3D%5Ccsc%20%5Ctheta)
You can observe that angle 1 and angle with 47° are inside a parallelogram.
Consider that the sum of the internal angles of a parallelogram is 360°.
Moreover, consider that the angle at the top right of the parallogram is congruent with the angle of 47°, then, such an angle is if 47°.
Consider that angle down right side is congruent with angle 1, then, they have the same measure.
You can write the previous situation in the following equation:
47 + 47 + ∠1 + ∠1 = 360 simplify like terms
94 + 2∠1 = 360 subtract both sides by 94
2∠1 = 360 - 94
2∠1 = 266 divide by 2 both sides
∠1 = 266/2
∠1 = 133
Hence, the measure of angle 1 is m∠1 = 133°
The diameter is the distance from one side of a circle to the other, if you cross through the center. The circumference is the distance around the circle. The circumference is equal to two time pi time the radius (C=2*pi*r)
Answer:
Option C
The length of RT is 14
Step-by-step explanation:
For a given Right Triangle
m∠R = 90°, RG = 17, TG = 22
Now, <u>By Pythagoras Theorem</u>
(RT)² + (RG)² = (TG)²
(RT)² = (TG)² - (RG)²
(RT)² = (22)² - (17)²
(RT)² = 484 - 289
(RT)² = 195
RT = √195
RT = √195 = 13.96 = 14
Thus, The length of RT is 14
<u>-TheUnknownScientist</u>
Step-by-step explanation:
10. |-41|= 41
12. -|1.5|= -1.5