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3 years ago

Find the exact value of tan(θ + φ) given that sin θ = 4/5 and sin φ = 5/13and that θ and φ are between 0 and π/2. Note these ang

les are Pythagorean Triples.

Mathematics

1 answer:

MArishka [77]3 years ago

6 0

$\sin\theta=\dfrac45\implies\cos\theta=\dfrac35$
$\sin\varphi=\dfrac5{13}\implies\cos\varphi=\dfrac{12}{13}$

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac45$
$\tan\varphi=\dfrac{\sin\varphi}{\cos\varphi}=\dfrac5{12}$

$\tan(\theta+\varphi)=\dfrac{\tan\theta+\tan\varphi}{1-\tan\theta\tan\varphi}=\dfrac{63}{16}$

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krok68 [10]

The solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

<h3>How to solve the triangle?</h3>

The figure is not given;

However, the question can still be solved without it

The given parameters are:

a = 31, b = 23, and c = 20

Calculate angle A using the following law of cosine

a² = b² + c² - 2bc * cos(A)

So, we have:

31² = 23² + 20² - 2 * 23 * 20 * cos(A)

Evaluate

961 = 929 - 920 * cos(A)

Subtract 929 from both sides

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Divide both sides by -920

cos(A) = -0.0348

Take the arc cos of both sides

A = 92.0

Calculate angle B using the following law of sine

a/sin(A) = b/sin(B)

So, we have:

31/sin(92) = 23/sin(B)

This gives

31.0189 = 23/sin(B)

Rewrite as:

sin(B) =23/31.0189

Evaluate

sin(B) =0.7415

Take arc sin of both sides

B = 47.9

Calculate angle C using:

C = 180 - 92.0 - 47.9

Evaluate

C = 40.1

Hence, the solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

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3 years ago

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Answer:

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p(X<x) = 0.308538 + 0.95

= 1.258538

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= -2.58

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3 years ago