Answer:
Explanation:
Do you know SOHCAHTOA
Sin = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent
#1
We have to find cos(x) = adjacent/hypotenuse
![cos(x) = adj/hyp\\=(24)/(26) = (12)/(13)](https://img.qammunity.org/2021/formulas/mathematics/high-school/jnq689tr8qolonzjj24z33fe7ily243q60.png)
#2:
We are given an angle of 30 degrees and an opposite side of 15
We need to find the adjacent side, so we can use Tangent
![tan(30) = (15)/(adj)](https://img.qammunity.org/2021/formulas/mathematics/high-school/bplmsb2z7h55hfzg7565lzyjvyd1fdxdp7.png)
![adj = (15)/(tan(30)) = 25.98 = 26](https://img.qammunity.org/2021/formulas/mathematics/high-school/q0q2bznbet4275l62wr0re0yy31m3tmubn.png)
#3
We are given an angle and an opposite side and we have to solve for hypotenuse.
We can use sin
![sin(43) = (16)/(x) \\x = (16)/(sin(43)) = 23.46 = 23.5](https://img.qammunity.org/2021/formulas/mathematics/high-school/ax7mvupeih6b4qangwh6crfe751tb759fv.png)
#4:
We are given two sides, we have to find the angle. We are given an opposite side and an adjacent side, so we can use arctangent (
, but not 1/tan(x))
![tan(x) = (36)/(19) \\arctan(36/19) = x\\x = 62.1759](https://img.qammunity.org/2021/formulas/mathematics/high-school/dgirsu82iypdprqmntao4ikupr0ohd3lxl.png)
#5
We are given an opposite side and the hypotenuse, we can use sin
![sin(x) = (19)/(28)\\x = arcsin(19/28) = 42.73 = 43](https://img.qammunity.org/2021/formulas/mathematics/high-school/wpfaqr6vx8c5rksalv1wfv8y6xejr5qg4x.png)