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Ksenya-84 [330]
3 years ago
7

Work out the size of angle x

Mathematics
1 answer:
Misha Larkins [42]3 years ago
6 0

Answer:

13

Step-by-step explanation:

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Given the function value of the acute angle find the other five trigonometric function values cos a= Sqrt 7/7
PilotLPTM [1.2K]
Well, we know the angle is acute, that means is less than 90°, meaning is in the first quadrant, that means the "x" or adjacent side as well as the "y" or opposite side, are both positive.

\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\\\\
-------------------------------\\\\
cos(a)=\cfrac{\sqrt{7}}{7}\cfrac{\leftarrow adjacent}{\leftarrow hypotenuse}\quad \textit{now, let's find the \underline{opposite}}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}

\bf \pm\sqrt{7^2-(\sqrt{7})^2}=b\implies \pm\sqrt{49-7}=b\implies \pm\sqrt{42}=b
\\\\\\
\textit{now, which is it, the + or -? well, we're in the 1st quadrant, is }\sqrt{42}


\bf 
\textit{now that you know all three sides,  just plug them in}
\\\\\\
sin(\theta)=\cfrac{opposite}{hypotenuse}
\qquad 
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}
\\\\\\
% cotangent
cot(\theta)=\cfrac{adjacent}{opposite}
\qquad 
% cosecant
csc(\theta)=\cfrac{hypotenuse}{opposite}
\quad 
% secant
sec(\theta)=\cfrac{hypotenuse}{adjacent}
3 0
3 years ago
Giving 20 pts!!
kvasek [131]
Right ankle is exactly 90 degrees, while obtuse is more than, and acute is less than

4 0
3 years ago
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Help me match please!!! it’s for a grade
pochemuha

Answer:

number 2

Step-by-step explanation:

8 0
3 years ago
What is the highest common factor of 12 and 47​
icang [17]
The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 47 are: 1, 47

Then the greatest common factor is 1.


Hope this helps *smiles*
8 0
3 years ago
Find the radius of a circle in which an inscribed square has a side of 8 inches.​
Semenov [28]

Answer:

4\sqrt{2} =5.66

Step-by-step explanation:

The square is in the circle, so the diameter is the diagonal line of the square. This divides the square into two right triangles.

Two sides of the right triangle equal 8. This qualifies it as a special right triangle. This triangle has two sides that = x (in this case 8) and the hypotenuse is x\sqrt{2}.

Substitute 8 in for x.

8\sqrt{2} is the diameter, so we divide in half to get the radius = 4\sqrt{2}

7 0
3 years ago
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