Mathematics, 20.09.2019 13:30 alanahjones63

Question in picture
a) 16/63
b)-16/63
c) 63/16
d) -63/16

Question in picturea) 16/63b)-16/63c) 63/16d) -63/16

Answers: 1

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Answer from: Arealbot

ANSWER
$\tan(x + y) = - \frac{63}{16}$

EXPLANATION

We were given that,

$\csc(x) = \frac{5}{3}$

This implies that,

$\sin(x) = \frac{3}{5}$

We use the Pythagorean identity

$\sin^{2} (x) + \cos^{2} (x)= 1$
to get,

$\cos(x) = \sqrt{1 - ( { \frac{3}{5} })^{2}} = \frac{4}{5}$

We were also given that,

$\cos(y) = \frac{5}{13}$

This means that,

$\sin(y) = \sqrt{1 - {( \frac{5}{13}) }^{2} } = \frac{12}{13}$

This is because,

$0 < \: x \: < \frac{\pi}{2}$

$0 < \: y \: < \frac{\pi}{2}$

This angles are in the first quadrant so we pick the positive values.

$\tan(x + y) = \frac{ \sin(x + y) }{ \cos(x + y) }$

$\tan(x + y) = \frac{ \sin(x ) \cos(y) + \sin(y) \cos(x) }{ \cos(x) \cos(y) - \sin(x) \sin(y) }$

$\tan(x + y) = \frac{ \frac{3}{5} \times \frac{5}{13} + \frac{12}{13} \times \frac{4}{5} }{ \frac{4}{5} \times \frac{5}{13} - \frac{3}{5} \times \frac{12}{13} }$

$\tan(x + y) = - \frac{63}{16}$

The correct answer is D

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

Answer from: Quest

1.30

step-by-step explanation:

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Question in picture
a) 16/63
b)-16/63
c) 63/16
d) -63/16
...

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