Question

I posted this again because someone said they couldn’t see the picture.

Answer 1

Answer:

$a=\dfrac{5}{6}=0.83\:\: \sf (2\:d.p.)$

$c=\dfrac{13}{6}=2.17\:\:\sf(2\:d.p.)$

Step-by-step explanation:

Tan trigonometric ratio

$\sf \tan(\theta)=\dfrac{O}{A}$

where:

• $\theta$ is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

Therefore, from inspection of the given triangle:

$\implies \tan A=\dfrac{a}{b}$

$\textsf{If }\: \tan A=\dfrac{5}{12}\:\:\textsf{ and }\:\:b=2\:\:\textsf{then}:$

$\implies \dfrac{a}{2}=\dfrac{5}{12}$

$\implies 12a=5 \cdot 2$

$\implies 12a=10$

$\implies a=\dfrac{10}{12}$

$\implies a=\dfrac{5}{6}$

Pythagoras Theorem explains the relationship between the three sides of a right triangle.

  $a^2+b^2=c^2$

where:

• a and b are the legs of the right triangle.

• c is the hypotenuse (longest side) of the right triangle.

Substitute the value of b and the found value of a into the formula and solve for c:

$\implies \left(\dfrac{5}{6}\right)^2+2^2=c^2$

$\implies \dfrac{25}{36}+4=c^2$

$\implies c^2=\dfrac{169}{36}$

$\implies c=\sqrt{\dfrac{169}{36}}$

$\implies c=\dfrac{\sqrt{169}}{\sqrt{36}}$

$\implies c=\dfrac{13}{6}$

Learn more about right triangles here:

https://brainly.com/question/27648540

https://brainly.com/question/26861422

Answer 2

• tanA=Perpendicular/Base
• tanA=BC/AC
• tanA=a/b
• 5/12=a/b

• 5/12=a/2
• 5/6=a
• a=0.83

Now

• tanA=5/12
• A=arctan(5/12)

Then

• cosA=Base/Hypotenuse
• cosA=b/c
• c=b/cos(arctan(5/12))
• c=2/cos(arctan(5/12))
• c=2.17