Question

Need help with trigonometry

Answer 1

Answer:

$\sf \tan(A) & =\dfrac{9\sqrt{22}}{44}$

Step-by-step explanation:

If angle C is the right angle, then side c is the hypotenuse.

Use Pythagoras' Theorem $a^2+b^2=c^2$ to find the length of side a:

Given:

• b = 2√22
• c = 13

$\implies a^2+(2 \sqrt{22})^2=13^2$

$\implies a^2+88=169$

$\implies a^2=81$

$\implies a=\sqrt{81}$

$\implies a=9$

Tan Trig 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

Given:

• $\theta$ = A
• O = side opposite angle A = a = 9
• A = side adjacent angle A = b = 2√22

$\begin{aligned}\implies \sf \tan(A) & =\dfrac{9}{2\sqrt{22}}\\\\ & =\dfrac{9}{2\sqrt{22}} \times \dfrac{\sqrt{22}}{\sqrt{22}}\\\\ & = \dfrac{9\sqrt{22}}{44} \end{aligned}$

Answer 2

Answer:

$\boxed{ \sf \bold{tanA = \frac{9}{2\sqrt{22} } }}$

Given:

• c = 13

• b = 2√22

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Formula's:

• tan(x) = opposite/adjacent     :  tane rule

• a² + b² = c²     :  Pythagoras Theorem

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To find Tan A, first find opposite side of angle A and adjacent side which is already given of 2√22

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Opposite side:

• (2√22)² + b² = 13²

• b² = 169 - 88

• b² = 81

• b = √81

• b = 9

Now find tan A:

tanA = 9/2√22