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3 years ago

HELP PLEASEE i need it

Mathematics

1 answer:

Soloha48 [4]3 years ago

7 0

Answer:

See explanation

Step-by-step explanation:

1st photo:

x = $\sqrt{15}$

$\frac{x}{5} = \frac{3}{x}$

$x^{2}$ = 15

x = $\sqrt{15}$

2nd photo:

(a) GEH ~ FGH ~ FEG

similar triangles, use similar corners in the right order

(b) $\frac{FE}{GE} = \frac{GE}{EH}$ AND $\frac{FH}{GH} = \frac{GH}{HE}$

similar triangles, use similar sides in proportion

3rd photo:

x = 4.5 or 4 1/2

$\frac{x}{3} = \frac{3}{2}$

2x = 9

x = 4.5 or 4 1/2

4th photo:

Length of string = 118.2 ft

sin(40) = 76/x

x = 76/sin(40) = 118.2

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pishuonlain [190]

Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

$\cos{\theta} = \pm \frac{2\sqrt{2}}{3}$

$\tan{\theta} = \pm \frac{\sqrt{2}}{4}$

<h3>What is the trigonometric identity using in this problem?</h3>

The identity that relates the sine squared and the cosine squared of the angle, as follows:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

In this problem, we have that the sine is given by:

$\sin{\theta} = \frac{1}{3}$

Hence, applying the identity, the cosine is given as follows:

$\cos^2{\theta} = 1 - \sin^2{\theta}$

$\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2$

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The tangent is given by the sine divided by the cosine, hence:

$\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

$\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}$

$\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$\tan{\theta} = \pm \frac{\sqrt{2}}{4}$

More can be learned about trigonometric identities at brainly.com/question/24496175

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