Answer:
Part 1) ![b=8.2\ units](https://tex.z-dn.net/?f=b%3D8.2%5C%20units)
Part 2) ![a=10.1\ units](https://tex.z-dn.net/?f=a%3D10.1%5C%20units)
Part 3)
and ![C=90\°](https://tex.z-dn.net/?f=C%3D90%5C%C2%B0)
Step-by-step explanation:
see the attached figure with letters to better understand the problem
step 1
Find the side b
we know that
In the right triangle ABC
The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)
![sin(B)=AC/AB](https://tex.z-dn.net/?f=sin%28B%29%3DAC%2FAB)
we have
![AB=c=13\ units](https://tex.z-dn.net/?f=AB%3Dc%3D13%5C%20units)
![AC=b](https://tex.z-dn.net/?f=AC%3Db)
![B=39\°](https://tex.z-dn.net/?f=B%3D39%5C%C2%B0)
substitute
![sin(39\°)=b/13](https://tex.z-dn.net/?f=sin%2839%5C%C2%B0%29%3Db%2F13)
solve for b
![b=(13)sin(39\°)](https://tex.z-dn.net/?f=b%3D%2813%29sin%2839%5C%C2%B0%29)
![b=8.2\ units](https://tex.z-dn.net/?f=b%3D8.2%5C%20units)
step 2
Find the side a
we know that
In the right triangle ABC
The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)
![cos(B)=BC/AB](https://tex.z-dn.net/?f=cos%28B%29%3DBC%2FAB)
we have
![AB=c=13\ units](https://tex.z-dn.net/?f=AB%3Dc%3D13%5C%20units)
![BC=a](https://tex.z-dn.net/?f=BC%3Da)
![B=39\°](https://tex.z-dn.net/?f=B%3D39%5C%C2%B0)
substitute
![cos(39\°)=a/13](https://tex.z-dn.net/?f=cos%2839%5C%C2%B0%29%3Da%2F13)
solve for a
![a=(13)cos(39\°)](https://tex.z-dn.net/?f=a%3D%2813%29cos%2839%5C%C2%B0%29)
![a=10.1\ units](https://tex.z-dn.net/?f=a%3D10.1%5C%20units)
step 3
Find the measure of angle A
we know that
In the right triangle ABC
----> is a right angle
![B=39\°](https://tex.z-dn.net/?f=B%3D39%5C%C2%B0)
∠A+∠B=90° ------> by complementary angles
substitute the given value
![A+39\°=90\°](https://tex.z-dn.net/?f=A%2B39%5C%C2%B0%3D90%5C%C2%B0)
![A=90\°-39\°](https://tex.z-dn.net/?f=A%3D90%5C%C2%B0-39%5C%C2%B0)
![A=51\°](https://tex.z-dn.net/?f=A%3D51%5C%C2%B0)
The value of x is 5 by using external angle
Answer:
The trigonometric ratios are presented below:
![\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20%5Cfrac%7BAC%7D%7B%5Csqrt%7BAC%5E%7B2%7D%20%2B%20BC%5E%7B2%7D%7D%7D)
![\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%20%5Cfrac%7BBC%7D%7B%5Csqrt%7BAC%5E%7B2%7D%20%2B%20BC%5E%7B2%7D%7D%7D)
![\cot \theta = \frac{BC}{AC}](https://tex.z-dn.net/?f=%5Ccot%20%5Ctheta%20%3D%20%5Cfrac%7BBC%7D%7BAC%7D)
![\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}](https://tex.z-dn.net/?f=%5Csec%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csqrt%7BAC%5E%7B2%7D%2BBC%5E%7B2%7D%7D%7D%7BBC%7D)
![\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}](https://tex.z-dn.net/?f=%5Ccsc%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csqrt%7BAC%5E%7B2%7D%2BBC%5E%7B2%7D%7D%7D%7BAC%7D)
Step-by-step explanation:
From Trigonometry we know the following definitions for each trigonometric ratio:
Sine
(1)
Cosine
(2)
Tangent
(3)
Cotangent
(4)
Secant
(5)
Cosecant
(6)
Where:
- Adjacent leg.
- Opposite leg.
- Hypotenuse.
The length of the hypotenuse is determined by the Pythagorean Theorem:
![h = \sqrt{x^{2}+y^{2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D)
If
and
, then the trigonometric ratios are presented below:
![\sin \theta = \frac{AC}{\sqrt{AC^{2} + BC^{2}}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20%5Cfrac%7BAC%7D%7B%5Csqrt%7BAC%5E%7B2%7D%20%2B%20BC%5E%7B2%7D%7D%7D)
![\cos \theta = \frac{BC}{\sqrt{AC^{2} + BC^{2}}}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%20%5Cfrac%7BBC%7D%7B%5Csqrt%7BAC%5E%7B2%7D%20%2B%20BC%5E%7B2%7D%7D%7D)
![\cot \theta = \frac{BC}{AC}](https://tex.z-dn.net/?f=%5Ccot%20%5Ctheta%20%3D%20%5Cfrac%7BBC%7D%7BAC%7D)
![\sec \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{BC}](https://tex.z-dn.net/?f=%5Csec%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csqrt%7BAC%5E%7B2%7D%2BBC%5E%7B2%7D%7D%7D%7BBC%7D)
![\csc \theta = \frac{\sqrt{AC^{2}+BC^{2}}}{AC}](https://tex.z-dn.net/?f=%5Ccsc%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csqrt%7BAC%5E%7B2%7D%2BBC%5E%7B2%7D%7D%7D%7BAC%7D)
Answer:
Step-by-step explanation:100 miles down the middle when you do pythagorean thearom.
Answer:
22 hours = hours travelling altogether
Step-by-step explanation:
11 x 2 = 22